[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/10543#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/10543","headline":"\u7acb\u65b9\u6839 – Wikipedia","name":"\u7acb\u65b9\u6839 – Wikipedia","description":"\u7acb\u65b9\u6839\uff08\u308a\u3063\u307d\u3046\u3053\u3093\u3001cubic root\u3001root of third power\uff09\u3068\u306f\u3001\u3042\u308b\u6570\u304c\u4e0e\u3048\u3089\u308c\u305f\u6642\u3001\u4e09\u4e57\u3057\u3066\u4e0e\u3048\u3089\u308c\u305f\u6570\u3068\u306a\u308b\u3088\u3046\u306a\u65b0\u305f\u306a\u6570\u3092\u6307\u3059\u3002\u4e09\u4e57\u6839\uff08\u3055\u3093\u3058\u3087\u3046\u3053\u3093\uff09\u3068\u3082\u3044\u3046\u3002 \u7a4d\u306e\u5b9a\u7fa9\u3055\u308c\u305f\u96c6\u5408 E \u3092\u56fa\u5b9a\u3057\u3066\u8003\u3048\u308b\u3002E \u306e\u5143 a \u306b\u5bfe\u3057\u3001a = x3 \u3092\u6e80\u305f\u3059 x \u2208 E \u304c\u5b58\u5728\u3059\u308b\u3068\u304d\u3001x \u306f 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root\u3001root of third power\uff09\u3068\u306f\u3001\u3042\u308b\u6570\u304c\u4e0e\u3048\u3089\u308c\u305f\u6642\u3001\u4e09\u4e57\u3057\u3066\u4e0e\u3048\u3089\u308c\u305f\u6570\u3068\u306a\u308b\u3088\u3046\u306a\u65b0\u305f\u306a\u6570\u3092\u6307\u3059\u3002\u4e09\u4e57\u6839\uff08\u3055\u3093\u3058\u3087\u3046\u3053\u3093\uff09\u3068\u3082\u3044\u3046\u3002  \u7a4d\u306e\u5b9a\u7fa9\u3055\u308c\u305f\u96c6\u5408 E \u3092\u56fa\u5b9a\u3057\u3066\u8003\u3048\u308b\u3002E \u306e\u5143 a \u306b\u5bfe\u3057\u3001a = x3 \u3092\u6e80\u305f\u3059 x \u2208 E \u304c\u5b58\u5728\u3059\u308b\u3068\u304d\u3001x \u306f E \u306b\u304a\u3051\u308b a \u306e\u7acb\u65b9\u6839\u3067\u3042\u308b\u3068\u3044\u3046\u3002\u307e\u305f\u3001\u7acb\u65b9\u6839\u3092\u6c42\u3081\u308b\u3053\u3068\u3092\u958b\u7acb\uff08\u304b\u3044\u308a\u3085\u3046\uff09\u3068\u3044\u3046\u3002a \u304c\u5b9f\u6570\u3067\u3042\u308c\u3070 a \u306e\u7acb\u65b9\u6839\u306f\u5b9f\u6570\u306e\u7bc4\u56f2\u306b\u5e38\u306b\u305f\u3060\u4e00\u3064\u5b58\u5728 \u3057\u3001\u305d\u308c\u3092 a3{displaystyle {sqrt[{3}]{a}}} \u3068\u8868\u3059\u3002  \u6b63\u306e\u6570 a \u306b\u5bfe\u3057\u3066\u3001\u2212a3=\u2212a3.{displaystyle {sqrt[{3}]{-a}}=-{sqrt[{3}]{a}}.}1 \u306e\u865a\u7acb\u65b9\u6839\u306e\u4e00\u3064\u3092 \u03c9 \u3068\u3059\u308b\u3068\u3001\u3082\u3046\u4e00\u3064\u306e\u865a\u7acb\u65b9\u6839\u306f \u03c92 \u3067\u3042\u308a\u3001\u03c9, \u03c92 \u306f\u3068\u3082\u306b 1 \u306e\u539f\u59cb\u51aa\u6839\u3067\u3042\u308b\u3002\u307e\u305f\u30011 + \u03c9 + \u03c92 = 0 \u304c\u6210\u308a\u7acb\u3064\u30021,\u03c9=\u221212+32i,\u03c92=\u221212\u221232i=\u03c9\u00af.{displaystyle 1,quad omega =-{frac {1}{2}}+{frac {sqrt {3}}{2}}i,quad omega ^{2}=-{frac {1}{2}}-{frac {sqrt {3}}{2}}i={overline {omega }}.}\u03c9=exp\u2061(i\u22c5(2\u03c03+2k\u03c0)),\u03c92=exp\u2061(i\u22c5(4\u03c03+2k\u03c0)),\u03c9\u00af=exp\u2061(i\u22c5(\u22122\u03c03+2k\u03c0)).{displaystyle omega =exp left(icdot left({frac {2pi }{3}}+2kpi right)right),quad omega ^{2}=exp left(icdot left({frac {4pi }{3}}+2kpi right)right),quad {overline {omega }}=exp left(icdot left({frac {-2pi }{3}}+2kpi right)right).}\u03c9+1=exp\u2061(i\u22c5(\u03c03+2k\u03c0))=\u2212\u03c92,\u03c9\u00af+1=exp\u2061(i\u22c5(\u2212\u03c03+2k\u03c0))=\u2212\u03c9.{displaystyle omega +1=exp left(icdot left({frac {pi }{3}}+2kpi right)right)=-omega ^{2},quad {overline {omega }}+1=exp left(icdot left({frac {-pi }{3}}+2kpi right)right)=-omega .}  1\u03c9=\u03c92,1\u03c92=\u03c9.{displaystyle {frac {1}{omega }}=omega ^{2},quad {frac {1}{omega ^{2}}}=omega .}\u03b1 \u304c 0 \u3067\u306a\u3044\u8907\u7d20\u6570\u306a\u3089\u3070\u3001\u03b1 \u306e\u7acb\u65b9\u6839\u306f\u5e38\u306b 3 \u500b\u3042\u308a\u3001\u305d\u308c\u3089\u306f\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u3067\u3001\u539f\u70b9 O \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 |\u03b1|3{displaystyle {sqrt[{3}]{|alpha |}}} \u306e\u5186\u306b\u5185\u63a5\u3059\u308b\u6b63\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u306b\u306a\u308b\u3002\u5177\u4f53\u7684\u306a\u6570[\u7de8\u96c6]  \u8907\u7d20\u6570\u306e\u51aa\u6839\u306e\u5e7e\u4f55\u5b66\u7684\u8868\u73fe\u8907\u7d20\u6570\u306e\u5834\u5408\u306f\u3001\u5b9f\u90e8\u304c\u6700\u5927\u306e\u3082\u306e\u3092\u4e3b\u8981\u6839\u3068\u3059\u308b\u3002z13=exp\u2061(13ln\u2061z).{displaystyle z^{frac {1}{3}}=exp left({frac {1}{3}}ln {z}right).}93=2.0800838230\u22ef{displaystyle {sqrt[{3}]{9}}=2.0800838230cdots }\u6975\u5f62\u5f0f\u3067\u306fz=rexp\u2061(i\u03b8){displaystyle z=rexp(itheta ),}\u3053\u3053\u3067 r\u306f\u975e\u8ca0\u306e\u5b9f\u6570\u3001\u03b8{displaystyle theta }\u306e\u5b9a\u7fa9\u57df\u306f\u4ee5\u4e0b\u3068\u3059\u308b\uff08\u504f\u89d2\u306f\u591a\u4fa1\u95a2\u6570\u306e\u305f\u3081\uff09\u3002\u2212\u03c0\u03c0{displaystyle -pi 3).{displaystyle {sqrt[{3}]{z}}={sqrt[{3}]{r}}exp left({frac {itheta }{3}}right).}\u221283{displaystyle {sqrt[{3}]{-8}}} \u306f 1+3i{displaystyle 1+{sqrt {3}}i}\uff08=83e\u03c0i3{displaystyle ={sqrt[{3}]{8}}e^{frac {pi i}{3}}}\uff09 \u304c\u4e3b\u8981\u6839\u3068\u306a\u308b\uff08-2\uff08=(1+3i)e2\u03c0i3{displaystyle =(1+{sqrt {3}}i)e^{frac {2pi i}{3}}}\uff09\u3067\u306f\u306a\u3044\uff09\u3002\u4e3b\u8981\u6839\u306e\u8907\u7d20\u6570\u306e\u504f\u89d2\u306e\u7bc4\u56f2\u306f\u4ee5\u4e0b\u3068\u306a\u308b\u3002\u2212\u03c03\u03c03{displaystyle -{frac {pi }{3}}(z)\u22650{displaystyle Im (z)geq 0}\u3001\u504f\u89d2 \u03b8=21\u2218{displaystyle theta =21^{circ }} \u306e\u4f8b\uff09z3=cos\u206121\u2218+isin\u206121\u22183=cos\u20617\u2218+isin\u20617\u2218{displaystyle {sqrt[{3}]{z}}={sqrt[{3}]{cos 21^{circ }+isin 21^{circ }}}=cos 7^{circ }+isin 7^{circ }}\u2212z3=\u2212cos\u206121\u2218\u2212isin\u206121\u22183=cos\u2061(\u2212159\u2218)+isin\u2061(\u2212159\u2218)3=cos\u2061(\u221253\u2218)+isin\u2061(\u221253\u2218)=\u2212\u03c9(cos\u20617\u2218+isin\u20617\u2218){displaystyle {begin{aligned}{sqrt[{3}]{-z}}={sqrt[{3}]{-cos 21^{circ }-isin 21^{circ }}}=&{sqrt[{3}]{cos(-159^{circ })+isin(-159^{circ })}}=&cos(-53^{circ })+isin(-53^{circ })=&-omega (cos 7^{circ }+isin 7^{circ })end{aligned}}}\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/10543#breadcrumbitem","name":"\u7acb\u65b9\u6839 – Wikipedia"}}]}]