为什么有人说复数可以看成向量?我觉得两者没有任何关系啊 为什么复数的几何意义是向量?有方向?

\u590d\u6570\u548c\u5411\u91cf\u662f\u5426\u53ef\u4ee5\u6bd4\u8f83\uff0c\u5982\u679c\u53ef\u4ee5\u6709\u4ec0\u4e48\u8054\u7cfb\u548c\u533a\u522b

\u4e0d\u53ef\u4ee5\u6bd4\u8f83\u3002
\u56e0\u4e3a\u590d\u6570\u662f\u5f62\u5982z=a+bi\uff08a,b\u5747\u4e3a\u5b9e\u6570\uff09\u7684\u6570\u79f0\u4e3a\u590d\u6570\uff0c\u5176\u4e2da\u79f0\u4e3a\u5b9e\u90e8\uff0cb\u79f0\u4e3a\u865a\u90e8\uff0ci\u79f0\u4e3a\u865a\u6570\u5355\u4f4d\u3002\u5f53z\u7684\u865a\u90e8\u7b49\u4e8e\u96f6\u65f6\uff0c\u5e38\u79f0z\u4e3a\u5b9e\u6570\uff1b\u5f53z\u7684\u865a\u90e8\u4e0d\u7b49\u4e8e\u96f6\u65f6\uff0c\u5b9e\u90e8\u7b49\u4e8e\u96f6\u65f6\uff0c\u5e38\u79f0z\u4e3a\u7eaf\u865a\u6570\u3002\u590d\u6570\u57df\u662f\u5b9e\u6570\u57df\u7684\u4ee3\u6570\u95ed\u5305\uff0c\u5373\u4efb\u4f55\u590d\u7cfb\u6570\u591a\u9879\u5f0f\u5728\u590d\u6570\u57df\u4e2d\u603b\u6709\u6839\u3002
\u5411\u91cf\uff08\u4e5f\u79f0\u4e3a\u6b27\u51e0\u91cc\u5f97\u5411\u91cf\u3001\u51e0\u4f55\u5411\u91cf\u3001\u77e2\u91cf\uff09\uff0c\u6307\u5177\u6709\u5927\u5c0f\u548c\u65b9\u5411\u7684\u91cf\u3002\u5b83\u53ef\u4ee5\u5f62\u8c61\u5316\u5730\u8868\u793a\u4e3a\u5e26\u7bad\u5934\u7684\u7ebf\u6bb5\u3002\u7bad\u5934\u6240\u6307\uff1a\u4ee3\u8868\u5411\u91cf\u7684\u65b9\u5411\uff1b\u7ebf\u6bb5\u957f\u5ea6\uff1a\u4ee3\u8868\u5411\u91cf\u7684\u5927\u5c0f\u3002\u4e0e\u5411\u91cf\u5bf9\u5e94\u7684\u91cf\u53eb\u505a\u6570\u91cf\uff08\u7269\u7406\u5b66\u4e2d\u79f0\u6807\u91cf\uff09\uff0c\u6570\u91cf\uff08\u6216\u6807\u91cf\uff09\u53ea\u6709\u5927\u5c0f\uff0c\u6ca1\u6709\u65b9\u5411\u3002

\u6269\u5c55\u8d44\u6599\uff1a
\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0c\u5206\u522b\u53d6\u4e0ex\u8f74\u3001y\u8f74\u65b9\u5411\u76f8\u540c\u7684\u4e24\u4e2a\u5355\u4f4d\u5411\u91cfi\uff0cj\u4f5c\u4e3a\u4e00\u7ec4\u57fa\u5e95\u3002a\u4e3a\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u5185\u7684\u4efb\u610f\u5411\u91cf\uff0c\u4ee5\u5750\u6807\u539f\u70b9O\u4e3a\u8d77\u70b9P\u4e3a\u7ec8\u70b9\u4f5c\u5411\u91cfa\u3002
\u7531\u5e73\u9762\u5411\u91cf\u57fa\u672c\u5b9a\u7406\u53ef\u77e5\uff0c\u6709\u4e14\u53ea\u6709\u4e00\u5bf9\u5b9e\u6570\uff08x,y\uff09\uff0c\u4f7f\u5f97a=xi+yj\uff0c\u56e0\u6b64\u628a\u5b9e\u6570\u5bf9(x,y)\u53eb\u505a\u5411\u91cfa\u7684\u5750\u6807\uff0c\u8bb0\u4f5ca=(x,y)\u3002\u8fd9\u5c31\u662f\u5411\u91cfa\u7684\u5750\u6807\u8868\u793a\u3002\u5176\u4e2d(x,y)\u5c31\u662f\u70b9P\u7684\u5750\u6807\u3002\u5411\u91cfa\u79f0\u4e3a\u70b9P\u7684\u4f4d\u7f6e\u5411\u91cf\u3002

\u8bf4\u5230\u5e95\uff0c\u6570\u5b66\u5c31\u662f\u4e00\u4e2a\u5de5\u5177\u3002\u590d\u6570\u5c31\u662f\u8fd9\u4e48\u89c4\u5b9a\u7684\u3002
\u7136\u540e\u548c\u5e73\u9762\u76842\u7ef4\u8c61\u9650\u6bd4\u8f83\u7c7b\u4f3c\uff0c\u7136\u540e\u7528\u5411\u91cf\u6765\u7c7b\u6bd4\uff0c\u4fbf\u4e8e\u7406\u89e3

\u590d\u6570\u662f\u6307\u80fd\u5199\u6210\u5982\u4e0b\u5f62\u5f0f\u7684\u6570a+bi,\u8fd9\u91cca\u548cb\u662f\u5b9e\u6570\uff0ci\u662f\u865a\u6570\u5355\u4f4d\u3002\u5728\u590d\u6570a+bi\u4e2d\uff0ca\u79f0\u4e3a\u590d\u6570\u7684\u5b9e\u90e8\uff0cb\u79f0\u4e3a\u590d\u6570\u7684\u865a\u90e8\uff0ci\u79f0\u4e3a\u865a\u6570\u5355\u4f4d\u3002\u5f53\u865a\u90e8\u7b49\u4e8e\u96f6\u65f6\uff0c\u8fd9\u4e2a\u590d\u6570\u5c31\u662f\u5b9e\u6570\uff1b\u5f53\u865a\u90e8\u4e0d\u7b49\u4e8e\u96f6\u65f6\uff0c\u8fd9\u4e2a\u590d\u6570\u79f0\u4e3a\u865a\u6570\uff0c\u590d\u6570\u7684\u5b9e\u90e8\u5982\u679c\u7b49\u4e8e\u96f6\uff0c\u5219\u79f0\u4e3a\u7eaf\u865a\u6570\u3002[1] \u7531\u4e0a\u53ef\u77e5\uff0c\u590d\u6570\u96c6\u5305\u542b\u4e86\u5b9e\u6570\u96c6\uff0c\u5e76\u4e14\u662f\u5b9e\u6570\u96c6\u7684\u6269\u5f20\u3002 \u590d\u6570\u662f\u7531\u610f\u5927\u5229\u7c73\u5170\u5b66\u8005\u5361\u5f53\u5728\u5341\u516d\u4e16\u7eaa\u9996\u6b21\u5f15\u5165\uff0c\u7ecf\u8fc7\u8fbe\u6717\u8d1d\u5c14\u3001\u68e3\u83ab\u5f17\u3001\u6b27\u62c9\u3001\u9ad8\u65af\u7b49\u4eba\u7684\u5de5\u4f5c\uff0c\u6b64\u6982\u5ff5\u9010\u6e10\u4e3a\u6570\u5b66\u5bb6\u6240\u63a5\u53d7\u3002
\u590d\u6570\u7684\u56db\u5219\u8fd0\u7b97\u89c4\u5b9a\u4e3a\uff1a\u52a0\u6cd5\u6cd5\u5219\uff1a\uff08a+bi\uff09+\uff08c+di\uff09=\uff08a+c\uff09+\uff08b+d\uff09i\uff1b\u51cf\u6cd5\u6cd5\u5219\uff1a\uff08a+bi\uff09\uff0d\uff08c+di\uff09=\uff08a\uff0dc\uff09+\uff08b\uff0dd\uff09i\uff1b\u4e58\u6cd5\u6cd5\u5219\uff1a\uff08a+bi\uff09\u00b7\uff08c+di\uff09=\uff08ac\uff0dbd\uff09+\uff08bc+ad\uff09i\uff1b\u9664\u6cd5\u6cd5\u5219\uff1a\uff08a+bi\uff09\u00f7\uff08c+di\uff09=[\uff08ac+bd\uff09/\uff08c²+d²\uff09]+[\uff08bc-ad\uff09/\uff08c²+d²\uff09]i.
\u4f8b\u5982\uff1a[\uff08a+bi\uff09+\uff08c+di\uff09]-[(a+c\uff09+\uff08b+d\uff09i]=0\uff0c\u6700\u7ec8\u7ed3\u679c\u8fd8\u662f0\uff0c\u4e5f\u5c31\u5728\u6570\u5b57\u4e2d\u6ca1\u6709\u590d\u6570\u7684\u5b58\u5728\u3002
[\uff08a+bi\uff09+\uff08c+di\uff09]-[(a+c\uff09+\uff08b+d\uff09i]=Z\u662f\u4e00\u4e2a\u51fd\u6570\u3002

复数只能在二维一下看成向量,二维以上就不行了

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