解题方法
1 . 下列命题为真命题的是( )
A.复数![]() ![]() |
B.在复平面内,复数![]() |
C.若i为虚数单位,n为正整数,则![]() |
D.复数z是方程![]() ![]() |
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2022-07-14更新
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495次组卷
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3卷引用:湖南省衡阳市衡南县2021-2022学年高一下学期期末数学试题(A卷)
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解题方法
2 . (1)已知a、b
R且满足(a-i)2-3bi=(1+i)(2-2ai),又z1=3-ai,z2=-3b+2i,求
的模与共轭虚数.
(2)i的正整数指数幂满足
=i,
=-1
=-i
=1(n
).如i=i,i2=-1,i3=-i,i4=1.请分析并写出i的正整数指数幂和、差规律,以此规律计算i+ i2+ i3+….+i2022 ①或i-i2+ i3-i4 +….-i2022 ②(注:要求只计算①与②之一)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02d44492b51b0e08208fdc0d1707025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de20dd6e41cad31ad8b2efd54cd3ca5.png)
(2)i的正整数指数幂满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a207dd5e7a8578b44c5108b057a739ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21eb8408abce1d5c923d1ec482ccfbb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729ab66e41e68d130540d517e0a96b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e35996fbfefca0b7083883a38bd63be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd9b7ec681035c141b64c997a579f87.png)
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