题目内容
已知复数![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_ST/0.png)
A.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_ST/1.png)
B.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_ST/2.png)
C.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_ST/3.png)
D.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_ST/4.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_ST/5.png)
【答案】分析:利用两个复数代数形式的乘除法,虚数单位i的幂运算性质,把复数化到最简形式,依据模的定义求出z的模.
解答:解:复数
=
=
=
+
,
∴复数z的模为
=
,
故选 A.
点评:本题考查复数的模的定义和求法,两个复数代数形式的乘除法,虚数单位i 的幂运算性质,两个复数相除,分子和分母同时除以分母的共轭复数.
解答:解:复数
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_DA/0.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_DA/1.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_DA/2.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_DA/3.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_DA/4.png)
∴复数z的模为
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_DA/5.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101222823010513906/SYS201311012228230105139001_DA/6.png)
故选 A.
点评:本题考查复数的模的定义和求法,两个复数代数形式的乘除法,虚数单位i 的幂运算性质,两个复数相除,分子和分母同时除以分母的共轭复数.
![](http://thumb.zyjl.cn/images/loading.gif)
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