题目内容
已知z1=2+i,z2=1-2i,则复数![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_ST/0.png)
A.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_ST/1.png)
B.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_ST/2.png)
C.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_ST/3.png)
D.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_ST/4.png)
【答案】分析:由z1=2+i,z2=1-2i,知
=2-i,由此能求出复数
的模.
解答:解:∵z1=2+i,z2=1-2i,
∴![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/2.png)
=![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/3.png)
=![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/4.png)
=![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/5.png)
=2+i-2i
=2-i,
∴复数
的模=
.
故选D.
点评:本题考查复数代数形式的混合运算,是基础题.解题时要认真审题,仔细解答,注意合理地进行等价转化.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/0.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/1.png)
解答:解:∵z1=2+i,z2=1-2i,
∴
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/2.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/3.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/4.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/5.png)
=2+i-2i
=2-i,
∴复数
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/6.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103173740796794285/SYS201311031737407967942002_DA/7.png)
故选D.
点评:本题考查复数代数形式的混合运算,是基础题.解题时要认真审题,仔细解答,注意合理地进行等价转化.
![](http://thumb.zyjl.cn/images/loading.gif)
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