设复数Z=a+bi （a＞0，b＞0），将一个骰子连续掷两次，先后得到的点数分别做为a，b，则使复数Z2为纯虚数 一颗骰子连续掷两次，朝上的点数依次为a、b，使a=2b的概率...

\u8bbez=a+bi\uff08a\uff0cb\u2208R\uff09\uff0c\u5c06\u4e00\u4e2a\u9ab0\u5b50\u8fde\u7eed\u629b\u63b7\u4e24\u6b21\uff0c\u7b2c\u4e00 \u6b21\u5f97\u5230\u7684\u70b9\u6570\u4e3aa\uff0c\u7b2c\u4e8c\u6b21\u5f97\u5230\u7684\u70b9\u6570\u4e3ab\uff0c\u5219\u4f7f\u590d\u6570z2

\u4f7f\u590d\u6570z2\u4e3a\u7eaf\u865a\u6570\uff0c\u90a3\u4e48z=a+bi\uff0ca\uff0cb\u2208R\uff0c\u5b83\u7684\u865a\u90e8\u548c\u5b9e\u90e8\u76f8\u7b49\uff0c\u5c31\u662f\u7b2c\u4e00\u6b21\u5f97\u5230\u7684\u70b9\u6570\u4e3aa\uff0c\u7b2c\u4e8c\u6b21\u5f97\u5230\u7684\u70b9\u6570\u4e3ab\uff0ca=b\uff0c\u8fd9\u6837\u7684a\u3001b\u53ea\u6709\uff0c\uff081\uff0c1\uff09\uff0c\uff082\uff0c2\uff09\uff0c\uff083\uff0c3\uff09\uff0c\uff084\uff0c4\uff09\uff0c\uff085\uff0c5\uff09\uff0c\uff086\uff0c6\uff096\u79cd\u4f7f\u590d\u6570z2\u4e3a\u7eaf\u865a\u6570\u7684\u6982\u7387\u4e3a\uff1aP=66\u00d76\uff1d16\u6545\u7b54\u6848\u4e3a\uff1a16

\u4e00\u9897\u9ab0\u5b50\u8fde\u7eed\u63b7\u4e24\u6b21\uff0c\u671d\u4e0a\u7684\u70b9\u6570\u4f9d\u6b21\u4e3aa\u3001b\uff0c\u5219a\uff0cb\u7684\u6240\u6709\u60c5\u51b5\u6709\uff081\uff0c1\uff09\uff081\uff0c2\uff09\uff081\uff0c3\uff09\uff081\uff0c4\uff09\uff081\uff0c5\uff09\uff081\uff0c6\uff09\uff082\uff0c1\uff09\uff082\uff0c2\uff09\uff082\uff0c3\uff09\uff082\uff0c4\uff09\uff082\uff0c5\uff09\uff082\uff0c6\uff09\uff083\uff0c1\uff09\uff083\uff0c2\uff09\uff083\uff0c3\uff09\uff083\uff0c4\uff09\uff083\uff0c5\uff09\uff083\uff0c6\uff09\uff084\uff0c1\uff09\uff084\uff0c2\uff09\uff084\uff0c3\uff09\uff084\uff0c4\uff09\uff084\uff0c5\uff09\uff084\uff0c6\uff09\uff085\uff0c1\uff09\uff085\uff0c2\uff09\uff085\uff0c3\uff09\uff085\uff0c4\uff09\uff085\uff0c5\uff09\uff085\uff0c6\uff09\uff086\uff0c1\uff09\uff086\uff0c2\uff09\uff086\uff0c3\uff09\uff086\uff0c4\uff09\uff086\uff0c5\uff09\uff086\uff0c6\uff09\u517136\u79cd\u7ed3\u679c\uff0c\u6bcf\u7ec4\u7ed3\u679c\u7b49\u53ef\u80fd\u51fa\u73b0\uff0c\u5c5e\u4e8e\u53e4\u5178\u6982\u7387\u8bb0\uff1a\u201c\u671d\u4e0a\u7684\u70b9\u6570\u4f9d\u6b21\u4e3aa\u3001b\uff0c\u4f7fa=2b\u201d\u4e3a\u4e8b\u4ef6A\uff0c\u5219A\u5305\u542b\u7684\u7ed3\u679c\u6709\uff1a\uff082\uff0c1\uff09\uff084\uff0c2\uff09\uff086\uff0c3\uff09\u51713\u79cd\u7ed3\u679c\u7531\u53e4\u5178\u6982\u7387\u7684\u8ba1\u7b97\u516c\u5f0f\u53ef\u5f97P\uff08A\uff09=336\uff1d112\u6545\u7b54\u6848\u4e3a\uff1a112

∵Z=a+bi，∴Z²=a²-b²+2abi，
要使复数Z²为纯虚数，需a=b
由题意可知总的基本事件共6×6=36个，
而符合条件的有（1，1），（2，2），（3，3），（4，4），（5，5），（6，6）共6种，
故使复数Z²为纯虚数的概率为：P=

6

36

=

1

6

，
故选A

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