{"id":1025,"date":"2024-01-30T12:20:37","date_gmt":"2024-01-30T06:20:37","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=1025"},"modified":"2024-11-26T15:42:09","modified_gmt":"2024-11-26T09:42:09","slug":"%e0%a6%9c%e0%a6%9f%e0%a6%bf%e0%a6%b2-%e0%a6%b8%e0%a6%82%e0%a6%96%e0%a7%8d%e0%a6%af%e0%a6%be-complex-numbers","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/%e0%a6%9c%e0%a6%9f%e0%a6%bf%e0%a6%b2-%e0%a6%b8%e0%a6%82%e0%a6%96%e0%a7%8d%e0%a6%af%e0%a6%be-complex-numbers\/","title":{"rendered":"\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be (Complex Numbers)"},"content":{"rendered":"\r\n<h2><span style=\"color: #008000;\"><b>\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u0995\u09bf? (Complex Number)<\/b><span style=\"font-weight: 400;\">:<\/span><\/span><\/h2>\r\n<p><span style=\"font-weight: 400;\">\u09ae\u09c2\u09b2\u09a6 \u0993 \u0985\u09ae\u09c2\u09b2\u09a6 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b8\u09c7\u099f \u09ae\u09bf\u09b2\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b8\u09c7\u099f \u0997\u09a0\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u09aa\u09c2\u09b0\u09cd\u09a3 \u09a7\u09b0\u09cd\u09ae \u09b9\u09b2\u09cb \u098f\u09b0 \u09ac\u09b0\u09cd\u0997 \u09b8\u09ac \u09b8\u09ae\u09af\u09bc \u0985\u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{-1},\u00a0\\sqrt{-4},\u00a0\\sqrt{-6}<\/span><\/span><span style=\"font-weight: 400;\"> \u09aa\u09cd\u09b0\u09ad\u09c3\u09a4\u09bf \u098f\u09b0 \u09ac\u09b0\u09cd\u0997 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">-1,\u00a0-4,\u00a0-6<\/span><\/span><span style=\"font-weight: 400;\"> \u09aa\u09cd\u09b0\u09ad\u09c3\u09a4\u09bf \u09af\u09be \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995\u0964 \u098f \u09a7\u09b0\u09a8\u09c7\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0989\u09a6\u09cd\u09ad\u09ac \u09b9\u09af\u09bc\u09c7\u099b\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">x^2+1=0,\u00a0x^2=4,\u00a0x^2+6=0......<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09aa\u09cd\u09b0\u09ad\u09c3\u09a4\u09bf \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7\u0964 \u098f \u099c\u09be\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u09c7\u09b0 \u099a\u09c7\u09b7\u09cd\u099f\u09be\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09af\u09c7 \u09b8\u0995\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09af\u09be \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be \u09a5\u09c7\u0995\u09c7 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09a4\u09be\u0987 \u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 (\u09ac\u09be \u099c\u099f\u09bf\u09b2) <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/academic\/10\/\">\u09b8\u0982\u0996\u09cd\u09af\u09be<\/a><\/span>\u0964<\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.youtube.com\/watch?v=ps7rYtaCgSs&amp;t=1s\" target=\"_blank\" rel=\"noopener\">\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be<\/a><\/span> \u09b9\u099a\u09cd\u099b\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09ac\u09b0\u09cd\u09a7\u09bf\u09a4 \u09b0\u09c2\u09aa, \u09af\u09be <span class=\"katex-eq\" data-katex-display=\"false\">(i=-1)<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u098f\u0995\u099f\u09bf \u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u098f\u0995\u0995\u09c7\u09b0 \u09b8\u0982\u09af\u09c1\u0995\u09cd\u09a4\u09bf\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 \u0997\u09a0\u09bf\u09a4\u0964 \u0996\u09cd\u09b0\u09bf\u09b8\u09cd\u099f\u09aa\u09c2\u09b0\u09cd\u09ac <\/span><span style=\"font-weight: 400;\">50<\/span><span style=\"font-weight: 400;\"> \u0985\u09ac\u09cd\u09a6\u09c7 \u0997\u09cd\u09b0\u09bf\u0995 \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6 \u0993 \u09aa\u09cd\u09b0\u0995\u09cc\u09b6\u09b2\u09c0 \u0986\u09b2\u09c7\u0995\u099c\u09be\u09a8\u09cd\u09a6\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0 \u09b9\u09c7\u09b0\u09a8 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09a7\u09be\u09b0\u09a3\u09be \u09a6\u09c7\u09a8\u0964 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09af\u09cb\u0997, \u09ac\u09bf\u09af\u09bc\u09cb\u0997, \u0997\u09c1\u09a3 \u098f\u09ac\u0982 \u09ad\u09be\u0997 \u09b8\u09b0\u09cd\u09ac\u09aa\u09cd\u09b0\u09a5\u09ae \u09aa\u09cd\u09b0\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09c7\u09a8 \u0987\u09a4\u09be\u09b2\u09bf\u09b0 \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6 Rafael Bombelli (1526-1572)\u0964 \u09a4\u09bf\u09a8\u09bf \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0986\u09a6\u09b0\u09cd\u09b6\u09b0\u09c2\u09aa <span class=\"katex-eq\" data-katex-display=\"false\">a+ib<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09c7\u09a8\u0964 <\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b0\u09c7\u09a8\u09c7 \u09a6\u09c7\u0995\u09be\u09b0\u09cd\u09a4\u09c7 \u098f\u09ac\u0982 1777 \u09b8\u09be\u09b2\u09c7 \u0985\u09af\u09bc\u09b2\u09be\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u099c\u09a8\u09cd\u09af <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span><\/span><span style=\"font-weight: 400;\"> \u09aa\u09cd\u09b0\u09a4\u09c0\u0995 \u0986\u09ac\u09bf\u09b7\u09cd\u0995\u09be\u09b0 \u0995\u09b0\u09c7\u09a8\u0964 1806 \u09b8\u09be\u09b2\u09c7 \u09b0\u09ac\u09be\u09b0\u09cd\u099f \u0986\u09b0\u0997\u09be\u0981 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 \u09b8\u09ae\u09a4\u09b2\u09c7 \u099a\u09bf\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u0989\u09aa\u09b8\u09cd\u09a5\u09be\u09aa\u09a8 \u0995\u09b0\u09c7\u09a8 \u09af\u09be Argand Diagram \u09a8\u09be\u09ae\u09c7 \u09aa\u09b0\u09bf\u099a\u09bf\u09a4\u0964 \u09aa\u09cd\u09b0\u0995\u09cc\u09b6\u09b2\u09c0 \u0993 \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0\u09b0\u09be \u09ac\u09c0\u09ae\u09c7\u09b0 \u09ac\u09c8\u09b6\u09bf\u09b7\u09cd\u099f\u09cd\u09af \u0993 \u0985\u09a8\u09c1\u09a8\u09be\u09a6 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span><\/span><span style=\"font-weight: 400;\"> (\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be) \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09c7\u09a8\u0964 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09c0 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5, \u09aa\u09be\u0987\u09aa\u09c7\u09b0 \u09ad\u09bf\u09a4\u09b0\u09c7 \u09aa\u09be\u09a8\u09bf\u09b0 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9, \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09bf\u0995 \u09b8\u09be\u09b0\u09cd\u0995\u09bf\u099f, \u09b0\u09c7\u09a1\u09bf\u0993 \u09a4\u09b0\u0999\u09cd\u0997 \u09aa\u09cd\u09b0\u09c7\u09b0\u09a3 \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u0985\u09ad\u09bf\u09a8\u09ac \u09b8\u09ae\u09b8\u09cd\u09af\u09be\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u09c7\u0964 \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u09ae\u099c\u09be\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09be\u09b0 \u09b9\u09b2\u09cb \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u0986\u09ac\u09bf\u09b7\u09cd\u0995\u09be\u09b0 \u09a8\u09be \u09b9\u09b2\u09c7 \u0986\u09ae\u09b0\u09be \u09ae\u09cb\u09ac\u09be\u0987\u09b2 \u09ab\u09cb\u09a8\u09c7 \u0995\u09a5\u09be \u09ac\u09b2\u09be \u0995\u09bf\u0982\u09ac\u09be \u09b0\u09c7\u09a1\u09bf\u0993 \u09b6\u09c1\u09a8\u09a4\u09c7 \u09aa\u09be\u09b0\u09a4\u09be\u09ae \u09a8\u09be\u0964<\/span><\/p>\r\n\r\n\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x, y \\epsilon R<\/span> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">i=\\sqrt{-1}<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">x+iy<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u0986\u0995\u09be\u09b0\u09c7\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09be \u09b9\u09df \u098f\u09ac\u0982 \u098f\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{Z}<\/span><\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09df\u0964<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6 \u0993\u09df\u09c7\u09b2\u09be\u09b0 \u201c<span class=\"katex-eq\" data-katex-display=\"false\">i<\/span><\/span><span style=\"font-weight: 400;\">\u201d \u09aa\u09cd\u09b0\u09a4\u09c0\u0995\u099f\u09bf\u09b0 \u09aa\u09cd\u09b0\u09b0\u09cd\u09ac\u09a4\u0995 \u09af\u09be\u09b0 \u09ac\u09b0\u09cd\u0997 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995\u0964<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\r\n\r\n\r\n<span class=\"katex-eq\" data-katex-display=\"false\">x+iy=z-\u098f\\; x=Real\\;\u00a0Part\\;\u00a0of\\;\u00a0z Re\u00a0z \\equiv (\u09ac\u09be\u09b8\u09cd\u09a4\u09ac\\; \u0985\u0982\u09b6)\\\\ y=Imaginary\\;\u00a0Part\\;\u00a0of\\;\u00a0z \\equiv Im\u00a0z (\u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995\\; \u0985\u0982\u09b6)<\/span>\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x=0<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">z<\/span><\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 Pure Imaginary Number (\u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u09b8\u0982\u0996\u09cd\u09af\u09be)<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09b2\u09be \u09b9\u09df\u0964<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">y=0<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">z<\/span><\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be \u09ac\u09b2\u09be \u09b9\u09df\u0964 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}=x+0.i<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09ac\u09be\u0989\u09b8 (Bause) \u09b8\u09b0\u09cd\u09ac\u09aa\u09cd\u09b0\u09a5\u09ae <span class=\"katex-eq\" data-katex-display=\"false\">x+iy<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u0986\u0995\u09be\u09b0\u09c7\u09b0 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09aa\u09cd\u09b0\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09c7\u09a8\u0964<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b8\u09c7\u099f\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{C}<\/span><\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09df\u0964 <\/span><\/li>\r\n<\/ul>\r\n\r\n\r\n<span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{C}=\\{z:z=x+iy;x,y\\epsilon \\mathbb{R}\\}\\\\ \\mathbb{R}\\subseteq \\mathbb{C}<\/span>\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" class=\"aligncenter wp-image-1178\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/10\/image-49.png\" alt=\"\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\" width=\"673\" height=\"398\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/10\/image-49.png 673w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/10\/image-49-300x177.png 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<h2>\u00a0<\/h2>\r\n<h2><span style=\"color: #008000;\"><b>\u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0995\u09cd\u09b0\u09ae\u099c\u09cb\u09dc \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be (Complex numbers as a sequence of real numbers)<\/b><span style=\"font-weight: 400;\">:\u00a0<\/span><\/span><\/h2>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">z=(x, y)<\/span> \u09af\u09c7\u0996\u09be\u09a8\u09c7- <span class=\"katex-eq\" data-katex-display=\"false\">Re(z)=x<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09ac\u0982<\/span><span style=\"font-weight: 400;\"> <span class=\"katex-eq\" data-katex-display=\"false\">Im(z)=y<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09a6\u09c1\u099f\u09bf \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be <span class=\"katex-eq\" data-katex-display=\"false\">z_1\\equiv (x_1,\u00a0y_1)<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">z_2\\equiv (x_2, y_2)<\/span><\/span><span style=\"font-weight: 400;\"> \u09b8\u09ae\u09be\u09a8 \u09b9\u09ac\u09c7 \u09af\u09a6\u09bf \u09a4\u09be\u09b0\u09be \u099c\u099f\u09bf\u09b2 \u09b8\u09ae\u09a4\u09b2\u09c7 \u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">(x_1, y_1)=(x_2,y_2)<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09df <\/span><span style=\"font-weight: 400;\">[<span class=\"katex-eq\" data-katex-display=\"false\">x_1=x_2,y_1=y_2<\/span><\/span><span style=\"font-weight: 400;\">]<\/span><span style=\"font-weight: 400;\">\u0964<\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf \u0986\u09b8\u09b2\u09c7<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf\u09b0 \u098f\u0995\u099f\u09be \u201cNatural Extension\u201d \u09ac\u09be \u201c\u09aa\u09cd\u09b0\u09be\u0995\u09c3\u09a4\u09bf\u0995 \u09aa\u09cd\u09b0\u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u201d\u0964<\/span><\/p>\r\n\r\n\r\n\r\n<h2><span style=\"color: #008000;\"><b>\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b0\u09c8\u0996\u09bf\u0995 \u09aa\u09cd\u09b0\u0995\u09be\u09b6-\u0986\u09b0\u09cd\u0997\u09a8\u09cd\u09a1\u09c7\u09b0 \u099a\u09bf\u09a4\u09cd\u09b0 (Argond\u2019s Diagram):\u00a0<\/b><\/span><\/h2>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\" style=\"text-align: center;\">\r\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" class=\"aligncenter wp-image-1180\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/10\/image-50.png\" alt=\"\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\" width=\"673\" height=\"399\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/10\/image-50.png 673w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/10\/image-50-300x178.png 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/>\r\n<figcaption><strong>\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b0\u09c8\u0996\u09bf\u0995 \u09aa\u09cd\u09b0\u0995\u09be\u09b6-\u0986\u09b0\u09cd\u0997\u09a8\u09cd\u09a1\u09c7\u09b0 \u099a\u09bf\u09a4\u09cd\u09b0 (Argond\u2019s Diagram)\u00a0<\/strong><\/figcaption>\r\n<\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span><span style=\"font-weight: 400;\"> \u0985\u0995\u09cd\u09b7\u0995\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0985\u0995\u09cd\u09b7 \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span><\/span><span style=\"font-weight: 400;\"> \u0985\u0995\u09cd\u09b7\u0995\u09c7 \u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u0985\u0995\u09cd\u09b7 \u09a7\u09b0\u09c7 \u09af\u09c7 \u09b8\u09ae\u09a4\u09b2\u09c7 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b8\u09ae\u09c2\u09b9\u0995\u09c7 \u099a\u09bf\u09a4\u09cd\u09b0\u09bf\u09a4 \u0995\u09b0\u09be \u09b9\u09df, \u09a4\u09be\u0995\u09c7 \u0986\u09b0\u09cd\u0997\u09a8\u09cd\u09a1\u09c7\u09b0 \u099a\u09bf\u09a4\u09cd\u09b0 \u09ac\u09b2\u09be \u09b9\u09df\u0964<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0985\u0982\u09b6 <\/span><span style=\"font-weight: 400;\">=<\/span><span style=\"font-weight: 400;\"> \u09ad\u09c2\u099c \u098f\u09ac\u0982 \u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u0985\u0982\u09b6 <\/span><span style=\"font-weight: 400;\">=<\/span><span style=\"font-weight: 400;\"> \u0995\u09cb\u099f\u09bf<\/span><\/p>\r\n\r\n\r\n\r\n<h2><span style=\"color: #008000;\"><b>\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b8\u09cd\u09a5\u09be\u09aa\u09a8 (Vector representation of complex numbers):<\/b><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/h2>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\" style=\"text-align: center;\">\r\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" class=\"aligncenter wp-image-1181\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/10\/image-51.png\" alt=\"\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\" width=\"673\" height=\"326\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/10\/image-51.png 673w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/10\/image-51-300x145.png 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/>\r\n<figcaption>\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09c2\u09aa<\/figcaption>\r\n<\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be <span class=\"katex-eq\" data-katex-display=\"false\">z=x+iy=(x,\u00a0y)<\/span><\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">OP<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u099a\u09bf\u09b9\u09cd\u09a8\u09bf\u09a4 \u0995\u09b0\u09be \u09af\u09be\u09df \u09af\u09be\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">O<\/span><\/span>\u00a0<b>\u0986\u09a6\u09bf<\/b> <b>\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/b><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span>\u00a0<b>\u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4<\/b> <b>\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/b><span style=\"font-weight: 400;\">\u0964<\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af <span class=\"katex-eq\" data-katex-display=\"false\">OP<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09b2\u09cb <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{OP}<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09be <span class=\"katex-eq\" data-katex-display=\"false\">(z=x+iy)<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09aa\u09b0\u09ae\u09ae\u09be\u09a8 \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">z=x+iy=\\vec{OP}<\/span><\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09ac\u09b2\u09be \u09b9\u09df\u0964<\/span><\/p>\r\n<hr \/>\r\n<p>&nbsp;<\/p>\r\n<p><em><strong>\u098f\u0987\u099a\u098f\u09b8\u09b8\u09bf \u0993 \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u09aa\u09b0\u09c0\u0995\u09cd\u09b7\u09be\u09b0\u09cd\u09a5\u09c0\u09a6\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u0995\u09cb\u09b0\u09cd\u09b8\u09b8\u09ae\u09c2\u09b9\u0983<\/strong><\/em><\/p>\r\n<ul>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-25-online-batch-2-bangla-english-ict\/\">HSC 25 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a \u09e8.\u09e6 (\u09ac\u09be\u0982\u09b2\u09be, \u0987\u0982\u09b0\u09c7\u099c\u09bf, \u09a4\u09a5\u09cd\u09af \u0993 \u09af\u09cb\u0997\u09be\u09af\u09cb\u0997 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4\u09bf)<\/a><\/span><\/li>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-26-online-batch-bangla-english-ict\/\">HSC 26 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ac\u09be\u0982\u09b2\u09be, \u0987\u0982\u09b0\u09c7\u099c\u09bf, \u09a4\u09a5\u09cd\u09af \u0993 \u09af\u09cb\u0997\u09be\u09af\u09cb\u0997 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4\u09bf)<\/a><\/span><\/li>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-2025-online-batch\/\">HSC 25 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ab\u09bf\u099c\u09bf\u0995\u09cd\u09b8, \u0995\u09c7\u09ae\u09bf\u09b8\u09cd\u099f\u09cd\u09b0\u09bf, \u09ae\u09cd\u09af\u09be\u09a5, \u09ac\u09be\u09df\u09cb\u09b2\u099c\u09bf)<\/a><\/span><\/li>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-2026-online-batch\/\">HSC 26 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ab\u09bf\u099c\u09bf\u0995\u09cd\u09b8, \u0995\u09c7\u09ae\u09bf\u09b8\u09cd\u099f\u09cd\u09b0\u09bf, \u09ae\u09cd\u09af\u09be\u09a5, \u09ac\u09be\u09df\u09cb\u09b2\u099c\u09bf)<\/a><\/span><\/li>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/medical-admission-course\/\">\u09ae\u09c7\u09a1\u09bf\u0995\u09c7\u09b2 \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/dhaka-university-a-unit-admission-course\/\">\u09a2\u09be\u0995\u09be \u09ad\u09be\u09b0\u09cd\u09b8\u09bf\u099f\u09bf A Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/dhaka-university-b-unit-admission-course\/\">\u09a2\u09be\u0995\u09be \u09ad\u09be\u09b0\u09cd\u09b8\u09bf\u099f\u09bf B Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/buet-ques-solve\/\">\u09ac\u09c1\u09df\u09c7\u099f \u0995\u09cb\u09b6\u09cd\u099a\u09c7\u09a8 \u09b8\u09b2\u09ad \u0995\u09cb\u09b0\u09cd\u09b8<\/a><\/span><\/li>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/gst-a-unit-admission-course\/\">\u0997\u09c1\u099a\u09cd\u099b A Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\r\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/gst-b-unit-admission-course\/\">\u0997\u09c1\u099a\u09cd\u099b B Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\r\n<\/ul>\r\n<hr \/>\r\n<p>&nbsp;<\/p>\r\n<p><em><strong>\u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u0995\u09bf\u09b2 \u09a1\u09c7\u09ad\u09c7\u09b2\u09aa\u09ae\u09c7\u09a8\u09cd\u099f \u0995\u09cb\u09b0\u09cd\u09b8\u09b8\u09ae\u09c2\u09b9\u0983<\/strong><\/em><\/p>\r\n<ul>\r\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/study-abroad-complete-guideline\/\">\u09ac\u09bf\u09a6\u09c7\u09b6\u09c7 \u0989\u099a\u09cd\u099a\u09b6\u09bf\u0995\u09cd\u09b7\u09be: Study Abroad Complete Guideline<\/a><\/span><\/li>\r\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/student-hacks\/\">Student Hacks<\/a><\/span><\/li>\r\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ielts-course\/\">IELTS Course by Munzereen Shahid<\/a><\/span><\/li>\r\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/english-grammar-course\/\">Complete English Grammar Course<\/a><\/span><\/li>\r\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ms-bundle\/\"> Microsoft Office 3 in 1 Bundle<\/a><\/span><\/li>\r\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ghore-boshe-freelancing\/\">\u0998\u09b0\u09c7 \u09ac\u09b8\u09c7 Freelancing<\/a><\/span><\/li>\r\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/facebook-marketing\/\">Facebook Marketing<\/a><\/span><\/li>\r\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/adobe-4-in-1-bundle\/\">Adobe 4 in 1 Bundle<\/a><\/span><\/li>\r\n<\/ul>\r\n<hr \/>\r\n<p>&nbsp;<\/p>\r\n<p style=\"text-align: center;\"><em>\u09e7\u09e6 \u09ae\u09bf\u09a8\u09bf\u099f \u09b8\u09cd\u0995\u09c1\u09b2\u09c7\u09b0 \u0995\u09cd\u09b2\u09be\u09b8\u0997\u09c1\u09b2\u09cb \u0985\u09a8\u09c1\u09b8\u09b0\u09a3 \u0995\u09b0\u09a4\u09c7 \u09ad\u09bf\u099c\u09bf\u099f: <span style=\"color: #993300;\"><strong><a style=\"color: #993300;\" href=\"https:\/\/10minuteschool.com\/?ref=https%3A%2F%2Fblog.10minuteschool.com%2Fwordpress%2F&amp;post_id=78178&amp;blog_category_id=700\">www.10minuteschool.com<\/a><\/strong><\/span><\/em><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>\u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u0995\u09bf? (Complex Number): \u09ae\u09c2\u09b2\u09a6 \u0993 \u0985\u09ae\u09c2\u09b2\u09a6 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b8\u09c7\u099f \u09ae\u09bf\u09b2\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b8\u09c7\u099f \u0997\u09a0\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u09aa\u09c2\u09b0\u09cd\u09a3 \u09a7\u09b0\u09cd\u09ae \u09b9\u09b2\u09cb \u098f\u09b0 \u09ac\u09b0\u09cd\u0997 \u09b8\u09ac \u09b8\u09ae\u09af\u09bc \u0985\u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09aa\u09cd\u09b0\u09ad\u09c3\u09a4\u09bf \u098f\u09b0 \u09ac\u09b0\u09cd\u0997 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 \u09aa\u09cd\u09b0\u09ad\u09c3\u09a4\u09bf \u09af\u09be \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995\u0964 \u098f \u09a7\u09b0\u09a8\u09c7\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0989\u09a6\u09cd\u09ad\u09ac \u09b9\u09af\u09bc\u09c7\u099b\u09c7<\/p>\n<p> <a class=\"redmore\" href=\"https:\/\/10minuteschool.com\/content\/%e0%a6%9c%e0%a6%9f%e0%a6%bf%e0%a6%b2-%e0%a6%b8%e0%a6%82%e0%a6%96%e0%a7%8d%e0%a6%af%e0%a6%be-complex-numbers\/\">Read More<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4268,3038,50,3026],"tags":[326,329,151,327,330,328,325,319,317,324,320,296,323,306,322,316,318,321],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/1025"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=1025"}],"version-history":[{"count":9,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/1025\/revisions"}],"predecessor-version":[{"id":16151,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/1025\/revisions\/16151"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=1025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=1025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=1025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}