{"id":6982,"date":"2021-07-23T23:21:10","date_gmt":"2021-07-23T14:21:10","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6982"},"modified":"2026-09-27T16:55:53","modified_gmt":"2026-09-27T07:55:53","slug":"complex-numbers","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/complex-numbers\/","title":{"rendered":"\ud589\ub82c\uacfc \ubcf5\uc18c\uc218"},"content":{"rendered":"<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 0\uc7a5 5\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; <span class=\"itc_viewcontents\">(<a href=\"..\/\">\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30<\/a>)<\/span><\/p>\n<\/div>\n<p>\ud589\ub82c\uacfc \ubcf5\uc18c\uc218\ub294 \ubcc4\uac1c\uc758 \uac1c\ub150\uc778 \uac83\ucc98\ub7fc \ubcf4\uc774\uc9c0\ub9cc \uc11c\ub85c \ubc00\uc811\ud55c \uad00\ub828\uc774 \uc788\ub2e4. \uc2e4\uc81c\ub85c \ubcf5\uc18c\uc218\ub294 \ud2b9\ubcc4\ud55c \ud615\ud0dc\uc758 \\(2\\times 2\\) \uc2e4\ud589\ub82c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc774 \uc808\uc5d0\uc11c\ub294 \\(2\\times 2\\) \ud589\ub82c\uc758 \uae30\ubcf8 \uc5f0\uc0b0\uc744 \uc0b4\ud3b4\ubcf8 \ub4a4 \uc774\ub97c \uc774\uc6a9\ud558\uc5ec \ubcf5\uc18c\uc218\ub97c \uc815\uc758\ud558\uc790.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ud589\ub82c<\/h2>\n<p><span class=\"defined\">\ud589\ub82c<\/span>(matrix)\uc774\ub780 \uc218\ub97c \uc9c1\uc0ac\uac01\ud615 \ubaa8\uc591\uc73c\ub85c \ubc30\uc5f4\ud55c \ub4a4 \uad04\ud638\ub85c \ubb36\uc5b4 \ub098\ud0c0\ub0b8 \uac83\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \\(2\\)\uac1c\uc758 \ud589\uacfc \\(2\\)\uac1c\uc758 \uc5f4\uc744 \uac00\uc9c4 \\(2\\times 2\\) \uc2e4\ud589\ub82c(real matrix)\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<br \/>\n\\[<br \/>\nA=<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\na_{11} &#038; a_{12}\\\\<br \/>\na_{21} &#038; a_{22}<br \/>\n\\end{array}<br \/>\n\\right].<br \/>\n\\]<br \/>\n\uc5ec\uae30\uc11c \\(a_{ij}\\)\ub294 \\(i\\)\uc9f8 \ud589 \\(j\\)\uc9f8 \uc5f4\uc758 <span class=\"defined\">\uc131\ubd84<\/span>(entry)\uc774\uba70, \uadf8 \uac12\uc740 \uc2e4\uc218\uc774\ub2e4.<\/p>\n<p>\\(A\\)\uc640 \\(B\\)\uac00 \\(2\\times 2\\) \ud589\ub82c\uc774\uace0<br \/>\n\\[<br \/>\nA=<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\na_{11} &#038; a_{12}\\\\<br \/>\na_{21} &#038; a_{22}<br \/>\n\\end{array}<br \/>\n\\right],<br \/>\n\\qquad<br \/>\nB=<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\nb_{11} &#038; b_{12}\\\\<br \/>\nb_{21} &#038; b_{22}<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\]<br \/>\n\ub77c\uace0 \ud558\uc790. \ubaa8\ub4e0 \\(i,j\\)\uc5d0 \ub300\ud558\uc5ec \\(a_{ij}=b_{ij}\\)\uc77c \ub54c \\(A=B\\)\ub77c\uace0 \ud55c\ub2e4.<\/p>\n<p>\\(k\\)\uac00 \uc2e4\uc218\uc77c \ub54c \\(k\\)\uc640 \ud589\ub82c \\(A\\)\uc758 <span class=\"defined\">\uc2a4\uce7c\ub77c\ubc30<\/span>(scalar multiplication)\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[<br \/>\nkA=<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\nka_{11} &#038; ka_{12}\\\\<br \/>\nka_{21} &#038; ka_{22}<br \/>\n\\end{array}<br \/>\n\\right].<br \/>\n\\]<br \/>\n\ub450 \ud589\ub82c\uc758 \ud569\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[<br \/>\nA+B=<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\na_{11}+b_{11} &#038; a_{12}+b_{12}\\\\<br \/>\na_{21}+b_{21} &#038; a_{22}+b_{22}<br \/>\n\\end{array}<br \/>\n\\right].<br \/>\n\\]\n<\/p>\n<p>\ub450 \ud589\ub82c\uc758 \uacf1 \\(AB\\)\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[<br \/>\nAB=<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\na_{11}b_{11}+a_{12}b_{21}<br \/>\n&#038;<br \/>\na_{11}b_{12}+a_{12}b_{22}<br \/>\n\\\\<br \/>\na_{21}b_{11}+a_{22}b_{21}<br \/>\n&#038;<br \/>\na_{21}b_{12}+a_{22}b_{22}<br \/>\n\\end{array}<br \/>\n\\right].<br \/>\n\\]<br \/>\n\uc989 \\(AB\\)\uc758 \\(ij\\)-\uc131\ubd84\uc740<br \/>\n\\[<br \/>\n(AB)_{ij}<br \/>\n=<br \/>\n\\sum_{k=1}^{2}a_{ik}b_{kj}<br \/>\n\\]<br \/>\n\uc774\ub2e4.<\/p>\n<p>\ud589\ub82c \\(A\\)\uc758 \ud589\uacfc \uc5f4\uc744 \uc11c\ub85c \ubc14\uafb8\uc5b4 \uc5bb\uc740 \ud589\ub82c<br \/>\n\\[<br \/>\nA^{\\mathrm{T}}<br \/>\n=<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\na_{11} &#038; a_{21}\\\\<br \/>\na_{12} &#038; a_{22}<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\]<br \/>\n\ub97c \\(A\\)\uc758 <span class=\"defined\">\uc804\uce58\ud589\ub82c<\/span>(transpose)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 0.5.1.<\/span><\/p>\n<p>\\(A,\\) \\(B,\\) \\(C\\)\uac00 \\(2\\times 2\\) \uc2e4\ud589\ub82c\uc77c \ub54c \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"bracket\">\n<li>\\(A+B=B+A\\).<\/li>\n<li>\\((A+B)+C=A+(B+C)\\).<\/li>\n<li>\\((AB)C=A(BC)\\).<\/li>\n<li>\\(A(B+C)=AB+AC\\).<\/li>\n<li>\\((A+B)C=AC+BC\\).<\/li>\n<\/ol>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>(1), (2)\ub294 \ud589\ub82c\uc758 \uac01 \uc131\ubd84\uc744 \ube44\uad50\ud558\uace0 \uc2e4\uc218\uc758 \ub367\uc148\uc5d0 \ub300\ud55c \uad50\ud658\ubc95\uce59\uacfc \uacb0\ud569\ubc95\uce59\uc744 \uc801\uc6a9\ud558\uba74 \uc5bb\uc5b4\uc9c4\ub2e4.<\/p>\n<p>(3) \\(A=[a_{ij}],\\) \\(B=[b_{ij}],\\) \\(C=[c_{ij}]\\)\ub77c\uace0 \ud558\uc790. \uc784\uc758\uc758 \\(i,j\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\n((AB)C)_{ij}<br \/>\n&#038;=<br \/>\n\\sum_{k=1}^{2}(AB)_{ik}c_{kj}\\\\<br \/>\n&#038;=<br \/>\n\\sum_{k=1}^{2}<br \/>\n\\left(<br \/>\n\\sum_{\\ell=1}^{2}a_{i\\ell}b_{\\ell k}<br \/>\n\\right)c_{kj}\\\\<br \/>\n&#038;=<br \/>\n\\sum_{\\ell=1}^{2}<br \/>\na_{i\\ell}<br \/>\n\\left(<br \/>\n\\sum_{k=1}^{2}b_{\\ell k}c_{kj}<br \/>\n\\right)\\\\<br \/>\n&#038;=<br \/>\n(A(BC))_{ij}.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c \\((AB)C=A(BC)\\)\uc774\ub2e4.<\/p>\n<p>(4) \uc784\uc758\uc758 \\(i,j\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\n(A(B+C))_{ij}<br \/>\n&#038;=<br \/>\n\\sum_{k=1}^{2}a_{ik}(b_{kj}+c_{kj})\\\\<br \/>\n&#038;=<br \/>\n\\sum_{k=1}^{2}a_{ik}b_{kj}<br \/>\n+<br \/>\n\\sum_{k=1}^{2}a_{ik}c_{kj}\\\\<br \/>\n&#038;=<br \/>\n(AB+AC)_{ij}.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c \\(A(B+C)=AB+AC\\)\uc774\ub2e4.<\/p>\n<p>(5)\ub3c4 \uac19\uc740 \ubc29\ubc95\uc73c\ub85c<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\n((A+B)C)_{ij}<br \/>\n&#038;=<br \/>\n\\sum_{k=1}^{2}(a_{ik}+b_{ik})c_{kj}\\\\<br \/>\n&#038;=<br \/>\n\\sum_{k=1}^{2}a_{ik}c_{kj}<br \/>\n+<br \/>\n\\sum_{k=1}^{2}b_{ik}c_{kj}\\\\<br \/>\n&#038;=<br \/>\n(AC+BC)_{ij}<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c \\((A+B)C=AC+BC\\)\uc774\ub2e4. <span class=\"qed\"><\/span><\/p>\n<\/div>\n<p>\uc77c\ubc18\uc801\uc73c\ub85c \ud589\ub82c\uc758 \ud569 \\(A+B\\)\ub294 \\(A\\)\uc640 \\(B\\)\uc758 \ud589\uc758 \uac1c\uc218\uc640 \uc5f4\uc758 \uac1c\uc218\uac00 \uac01\uac01 \uac19\uc744 \ub54c \uc815\uc758\ub41c\ub2e4. \ud589\ub82c\uc758 \uacf1 \\(AB\\)\ub294 \\(A\\)\uc758 \uc5f4\uc758 \uac1c\uc218\uc640 \\(B\\)\uc758 \ud589\uc758 \uac1c\uc218\uac00 \uac19\uc744 \ub54c \uc815\uc758\ub41c\ub2e4.<\/p>\n<p>\ud589\ub82c\uc758 \uacf1\uc148\uc740 \uc77c\ubc18\uc801\uc73c\ub85c \uad50\ud658\ubc95\uce59\uc744 \ub9cc\uc871\uc2dc\ud0a4\uc9c0 \uc54a\ub294\ub2e4. \uc989 \ub450 \ud589\ub82c \\(A,B\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\nAB=BA<br \/>\n\\]<br \/>\n\uac00 \ud56d\uc0c1 \uc131\ub9bd\ud558\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. \uadf8\ub7ec\ub098 \uc544\ub798\uc5d0\uc11c \uc815\uc758\ud560 \ubcf5\uc18c\uc218\uc5d0 \ud574\ub2f9\ud558\ub294 \ud2b9\ubcc4\ud55c \ud589\ub82c\ub4e4 \uc0ac\uc774\uc5d0\uc11c\ub294 \uacf1\uc148\uc758 \uad50\ud658\ubc95\uce59\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ubcf5\uc18c\uc218<\/h2>\n<p><span class=\"defined\">\ubcf5\uc18c\uc218<\/span>(complex number)\ub780 \ub2e4\uc74c\uacfc \uac19\uc740 \uaf34\uc758 \\(2\\times 2\\) \uc2e4\ud589\ub82c\uc744 \uc774\ub978\ub2e4.<br \/>\n\\[<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na &#038; -b\\\\<br \/>\nb &#038; a<br \/>\n\\end{array}<br \/>\n\\right],<br \/>\n\\qquad<br \/>\na,b\\in\\mathbb{R}.<br \/>\n\\]<br \/>\n\ubcf5\uc18c\uc218 \uc804\uccb4\uc758 \uc9d1\ud569\uc744 \\(\\mathbb{C}\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\ud2b9\ud788 \ubcf5\uc18c\uc218<br \/>\n\\[<br \/>\n\\boldsymbol{i}<br \/>\n=<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\n0 &#038; -1\\\\<br \/>\n1 &#038; 0<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\]<br \/>\n\uc744 <span class=\"defined\">\ud5c8\uc218\ub2e8\uc704<\/span>(imaginary unit)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\uac01 \uc2e4\uc218 \\(a\\)\ub97c \ubcf5\uc18c\uc218<br \/>\n\\[<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\na &#038; 0\\\\<br \/>\n0 &#038; a<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\]<br \/>\n\uc640 \ub3d9\uc77c\uc2dc\ud558\uae30\ub85c \ud558\uc790. \ud2b9\ud788 \uc2e4\uc218 \\(1\\)\uc740 \ud56d\ub4f1\ud589\ub82c<br \/>\n\\[<br \/>\n1=<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\n1 &#038; 0\\\\<br \/>\n0 &#038; 1<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\]<br \/>\n\uacfc \ub3d9\uc77c\uc2dc\ub41c\ub2e4. \uc774\ub54c<br \/>\n\\[<br \/>\n\\boldsymbol{i}^{\\,2}<br \/>\n=<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\n0 &#038; -1\\\\<br \/>\n1 &#038; 0<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\n0 &#038; -1\\\\<br \/>\n1 &#038; 0<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n=<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\n-1 &#038; 0\\\\<br \/>\n0 &#038; -1<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n=<br \/>\n-1.<br \/>\n\\]\n<\/p>\n<p>\ub530\ub77c\uc11c \uc784\uc758\uc758 \ubcf5\uc18c\uc218\ub294<br \/>\n\\[<br \/>\na+b\\boldsymbol{i},<br \/>\n\\qquad a,b\\in\\mathbb{R},<br \/>\n\\]<br \/>\n\uc758 \uaf34\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc2e4\uc81c\ub85c<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na &#038; -b\\\\<br \/>\nb &#038; a<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n&#038;=<br \/>\na<br \/>\n\\left[<br \/>\n\\begin{array}{cc}<br \/>\n1 &#038; 0\\\\<br \/>\n0 &#038; 1<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n+<br \/>\nb<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\n0 &#038; -1\\\\<br \/>\n1 &#038; 0<br \/>\n\\end{array}<br \/>\n\\right]\\\\<br \/>\n&#038;=<br \/>\na+b\\boldsymbol{i}.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\ub610\ud55c \uc774\ub7ec\ud55c \ud45c\ud604\uc740 \uc720\uc77c\ud558\ub2e4. \uc2e4\uc81c\ub85c<br \/>\n\\[<br \/>\na+b\\boldsymbol{i}<br \/>\n=<br \/>\nc+d\\boldsymbol{i}<br \/>\n\\]<br \/>\n\uc774\uba74 \uc774\uc5d0 \ub300\uc751\ud558\ub294 \ub450 \ud589\ub82c\uc758 \uc131\ubd84\uc774 \ubaa8\ub450 \uac19\uc73c\ubbc0\ub85c<br \/>\n\\[<br \/>\na=c,<br \/>\n\\qquad<br \/>\nb=d<br \/>\n\\]<br \/>\n\uc774\ub2e4.<\/p>\n<p>\\(z=a+b\\boldsymbol{i}\\)\uc774\uace0 \\(a,b\\in\\mathbb{R}\\)\uc77c \ub54c, \\(a\\)\ub97c \\(z\\)\uc758 <span class=\"defined\">\uc2e4\uc218\ubd80<\/span>(real part)\ub77c\uace0 \ubd80\ub974\uace0 \\(b\\)\ub97c \\(z\\)\uc758 <span class=\"defined\">\ud5c8\uc218\ubd80<\/span>(imaginary part)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\ubcf5\uc18c\uc218\uc758 \ud569\uacfc \uacf1\uc740 \ud589\ub82c\uc758 \ud569\uacfc \uacf1\uc73c\ub85c\ubd80\ud130 \uc5bb\uc5b4\uc9c4\ub2e4. \\(z_1=a_1+b_1\\boldsymbol{i}\\), \\(z_2=a_2+b_2\\boldsymbol{i}\\)\ub77c\uace0 \ud558\uba74<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\nz_1+z_2<br \/>\n&#038;=<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na_1 &#038; -b_1\\\\<br \/>\nb_1 &#038; a_1<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n+<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na_2 &#038; -b_2\\\\<br \/>\nb_2 &#038; a_2<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na_1+a_2 &#038; -(b_1+b_2)\\\\<br \/>\nb_1+b_2 &#038; a_1+a_2<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n(a_1+a_2)+(b_1+b_2)\\boldsymbol{i},<br \/>\n\\\\[10pt]<br \/>\nz_1z_2<br \/>\n&#038;=<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na_1 &#038; -b_1\\\\<br \/>\nb_1 &#038; a_1<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na_2 &#038; -b_2\\\\<br \/>\nb_2 &#038; a_2<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na_1a_2-b_1b_2 &#038; -(a_1b_2+a_2b_1)\\\\<br \/>\na_1b_2+a_2b_1 &#038; a_1a_2-b_1b_2<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n(a_1a_2-b_1b_2)<br \/>\n+<br \/>\n(a_1b_2+a_2b_1)\\boldsymbol{i}.<br \/>\n\\end{aligned}<br \/>\n\\]\n<\/p>\n<p>\ub9c8\uc9c0\ub9c9 \uc2dd\uc740 \\(z_1\\)\uacfc \\(z_2\\)\ub97c \uc11c\ub85c \ubc14\uafb8\uc5b4\ub3c4 \ubcc0\ud558\uc9c0 \uc54a\uc73c\ubbc0\ub85c<br \/>\n\\[<br \/>\nz_1z_2=z_2z_1<br \/>\n\\]<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c \uc77c\ubc18\uc801\uc778 \ud589\ub82c\uacfc \ub2ec\ub9ac \ubcf5\uc18c\uc218\uc5d0 \ud574\ub2f9\ud558\ub294 \uc774 \ud2b9\ubcc4\ud55c \ud589\ub82c\ub4e4\uc740 \uacf1\uc148\uc5d0 \ub300\ud558\uc5ec \uad50\ud658\ubc95\uce59\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ubcf5\uc18c\ucf24\ub808\uc640 \uc5ed\uc6d0<\/h2>\n<p>\\(z=a+b\\boldsymbol{i}\\)\uc77c \ub54c<br \/>\n\\[<br \/>\n\\overline{z}=a-b\\boldsymbol{i}<br \/>\n\\]<br \/>\n\ub97c \\(z\\)\uc758 <span class=\"defined\">\ubcf5\uc18c\ucf24\ub808<\/span>(complex conjugate)\ub77c\uace0 \ubd80\ub978\ub2e4. \ud589\ub82c\uc758 \uad00\uc810\uc5d0\uc11c \ubcf4\uba74<br \/>\n\\[<br \/>\nz=<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na &#038; -b\\\\<br \/>\nb &#038; a<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\nz^{\\mathrm{T}}<br \/>\n=<br \/>\n\\left[<br \/>\n\\begin{array}{rr}<br \/>\na &#038; b\\\\<br \/>\n-b &#038; a<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n=<br \/>\n\\overline{z}.<br \/>\n\\]<br \/>\n\uc989 \ubcf5\uc18c\uc218\uc5d0 \ud574\ub2f9\ud558\ub294 \ud589\ub82c\uc758 \uc804\uce58\ub294 \ubcf5\uc18c\ucf24\ub808\uc5d0 \ud574\ub2f9\ud55c\ub2e4.<\/p>\n<p>\ub610\ud55c<br \/>\n\\[<br \/>\nz\\overline{z}<br \/>\n=<br \/>\n(a+b\\boldsymbol{i})(a-b\\boldsymbol{i})<br \/>\n=<br \/>\na^2+b^2.<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c \\(z\\ne0\\)\uc774\uba74 \\(a\\)\uc640 \\(b\\)\uac00 \ub3d9\uc2dc\uc5d0 \\(0\\)\uc77c \uc218 \uc5c6\uc73c\ubbc0\ub85c<br \/>\n\\[<br \/>\na^2+b^2>0.<br \/>\n\\]<br \/>\n\uadf8\ub7ec\ubbc0\ub85c<br \/>\n\\[<br \/>\nz^{-1}<br \/>\n=<br \/>\n\\frac{a-b\\boldsymbol{i}}{a^2+b^2}<br \/>\n\\]<br \/>\n\ub85c \ub193\uc73c\uba74<br \/>\n\\[<br \/>\nzz^{-1}=z^{-1}z=1<br \/>\n\\]<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c \\(0\\)\uc774 \uc544\ub2cc \ubaa8\ub4e0 \ubcf5\uc18c\uc218\ub294 \uacf1\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc744 \uac00\uc9c4\ub2e4.<\/p>\n<p>\uc774\uc640 \uac19\uc774 \ubcf5\uc18c\uc218\ub294 \uc2e4\uc218\uc758 \ub367\uc148\uacfc \uacf1\uc148\uc758 \uc131\uc9c8\uc744 \uadf8\ub300\ub85c \uac00\uc9c0\uba74\uc11c<br \/>\n\\[<br \/>\n\\boldsymbol{i}^{\\,2}=-1<br \/>\n\\]<br \/>\n\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc0c8\ub85c\uc6b4 \uc218 \\(\\boldsymbol{i}\\)\ub97c \ud3ec\ud568\ud558\ub294 \uc218 \uccb4\uacc4\ub97c \uc774\ub8ec\ub2e4. \uc2e4\uc81c \uacc4\uc0b0\uc5d0\uc11c\ub294 \ubcf5\uc18c\uc218\ub97c \ud589\ub82c\ub85c \uc0dd\uac01\ud560 \ud544\uc694 \uc5c6\uc774, \uc2e4\uc218 \\(a,b\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\na+b\\boldsymbol{i}<br \/>\n\\]<br \/>\n\uc758 \uaf34\ub85c \ub098\ud0c0\ub0b4\uace0 \\(\\boldsymbol{i}^{\\,2}=-1\\)\uc744 \uc774\uc6a9\ud558\uc5ec \uacc4\uc0b0\ud558\uba74 \ub41c\ub2e4.<\/p>\n<p><!-- ##################################################################### --><br \/>\n<!--\n\n\n<h2 class=\"itc_h2\">\uc81c\ubaa9<\/h2>\n\n\n--><\/p>\n<p><!--\n\n\n\n<div class=\"theorem margintop2\">\n\n\n<p><span class=\"theorem\">\uc815\ub9ac 1.<\/span>\n\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<div class=\"proof\">\n\n\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n\n\n\n\n<p>\n\n<span class=\"qed\"><\/span><\/p>\n\n<\/div>\n\n\n\n\n########\n\n\u201c\u201d\n\u2018\u2019\n\n\n\n<div class=\"example\">\n\n\n<p><span class=\"example\">\ubcf4\uae30 1.<\/span>\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<h2 class=\"itc_h2\"><\/h2>\n\n\n\n--><\/p>\n<p><!--\n\n\n<div style=\"display: none; visibility: hidden;\">\n\\[\n\\newcommand{\\Hom}{{\\operatorname{Hom}}}\n\\newcommand{\\Mat}{{\\operatorname{Mat}}}\n\\newcommand{\\proj}{{\\operatorname{proj}}}\n\\newcommand{\\adj}{{\\operatorname{adj}}}\n\\]\n<\/div>\n\n\n--><\/p>\n<div class=\"box itc_prev_next_box\">\n<ul class=\"itc_ul\">\n<li class=\"itc_li_prev\">\uc55e\uc758 \uae00 : <a href=\"..\/real-numbers\">\uc2e4\uc218\uacc4<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/trigonometric-functions\">\uc0bc\uac01\ud568\uc218<\/a><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 0\uc7a5 5\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) \ud589\ub82c\uacfc \ubcf5\uc18c\uc218\ub294 \ubcc4\uac1c\uc758 \uac1c\ub150\uc778 \uac83\ucc98\ub7fc \ubcf4\uc774\uc9c0\ub9cc \uc11c\ub85c \ubc00\uc811\ud55c \uad00\ub828\uc774 \uc788\ub2e4. \uc2e4\uc81c\ub85c \ubcf5\uc18c\uc218\ub294 \ud2b9\ubcc4\ud55c \ud615\ud0dc\uc758 \\(2\\times 2\\) \uc2e4\ud589\ub82c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc774 \uc808\uc5d0\uc11c\ub294 \\(2\\times 2\\) \ud589\ub82c\uc758 \uae30\ubcf8 \uc5f0\uc0b0\uc744 \uc0b4\ud3b4\ubcf8 \ub4a4 \uc774\ub97c \uc774\uc6a9\ud558\uc5ec \ubcf5\uc18c\uc218\ub97c \uc815\uc758\ud558\uc790. \ud589\ub82c \ud589\ub82c(matrix)\uc774\ub780 \uc218\ub97c \uc9c1\uc0ac\uac01\ud615 \ubaa8\uc591\uc73c\ub85c \ubc30\uc5f4\ud55c \ub4a4 \uad04\ud638\ub85c \ubb36\uc5b4 \ub098\ud0c0\ub0b8 \uac83\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \\(2\\)\uac1c\uc758 \ud589\uacfc \\(2\\)\uac1c\uc758 \uc5f4\uc744 \uac00\uc9c4 \\(2\\times 2\\)&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":15,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-6982","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6982","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=6982"}],"version-history":[{"count":20,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6982\/revisions"}],"predecessor-version":[{"id":10127,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6982\/revisions\/10127"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6620"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=6982"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}