试题与答案

对任意复数z=x+yi（x，y∈R），i为虚数单位，则下列结论正确的是（ ） A．

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题型：选择题

题目：

对任意复数z=x+yi（x，y∈R），i为虚数单位，则下列结论正确的是（　　）
A．|z-
.
z
|=2y		B．z2=x2+y2C．|z-
.
z
|≥2x		D．|z|≤|x|+|y|

答案：

由于复数z=x+yi（x，y∈R），i为虚数单位，∴|z-

.
z
|=|2yi|=2|y|，故（A）错误．

由z2 =x2-y2-2xyi，故（B）错误．

由|z-

.
z
|=2|y|，不一定大于或等于2x，故（C）错误．

由|z|=

x2+ y2
≤
x2+y2+ 2|x||y|
=|x|+|y|，故（D）正确．

故选 D．

考点：复数的概念及几何意义
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