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1 . 已知
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f88173061d6ff36de8ec397aa73961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
A.![]() | B.![]() | C.1 | D.2 |
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2024-05-12更新
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1534次组卷
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4卷引用:单元测试A卷——第七章 复数
23-24高一下·全国·随堂练习
2 . 在复平面内,作出表示下列各复数的点和所对应的向量,求出其共轭复数以及模:
(1)
;
(2)
;
(3)
;
(4)
;
(5)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e591f4fb0e4345503aa3fca07fdf50.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6712e57e9176d4757aa86cc6825169c2.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b833bd0629ea933e98220d5f73a41f.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5053541d26bbaf1d80c50fab16d7aee5.png)
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23-24高一下·全国·课堂例题
3 . 计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23f6b96db3406054cd5824d82a50ece.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23f6b96db3406054cd5824d82a50ece.png)
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23-24高一下·全国·课前预习
4 . 复数的乘法
(1)复数的乘法法则
设
是任意两个复数,那么它们的积![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d355a0ab521aef48518679cf44ea27e7.png)
______________ .
(2)复数乘法的运算律
对于任意
,有
(1)复数的乘法法则
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7061314deb8ce88af5e218709a4ea17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d355a0ab521aef48518679cf44ea27e7.png)
(2)复数乘法的运算律
对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7dc24ba4bc1cae38927fcbce43e2419.png)
交换律 | ![]() |
结合律 | ![]() |
乘法对加法的分配律 | ![]() |
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23-24高一下·全国·课前预习
5 . 计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f552e9a55454b59d85161f57d6ff24.png)
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23-24高一下·全国·课前预习
6 . 复数加、减法的几何意义
如图,设在复平面内复数
对应的向量分别为
,以
为邻边作平行四边形,则与
对应的向量是_________ ,与
对应的向量是_____________ .
如图,设在复平面内复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a9e798dc024cf6d6815eb96a1f97b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95aa323fbc002e36c732051858419868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34b88f343ca5a4c29057465541b9cf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4e2b866b0043a32fc78326553841d3.png)
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23-24高一下·全国·课前预习
7 . 共轭复数
(1)定义:当两个复数的实部_________ ,虚部____________ 时,这两个复数叫做互为共轭复数.虚部不等于0的两个共轭复数也叫做共轭虚数.
(2)表示方法:复数z的共轭复数用
表示,即如果
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545141bbe7cc66d18946a129179d8df1.png)
__________ .
(1)定义:当两个复数的实部
(2)表示方法:复数z的共轭复数用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545141bbe7cc66d18946a129179d8df1.png)
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23-24高一下·全国·课前预习
8 . 复数的加、减法运算法则
设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe82a3f7f76832113ecf0e00803a589.png)
____________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35aa5256411e4bfe86bab7783a9022a6.png)
_____________ .
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0223af3b0dacb162f5a1fb7a01ee89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe82a3f7f76832113ecf0e00803a589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35aa5256411e4bfe86bab7783a9022a6.png)
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23-24高一下·全国·课前预习
9 . 复数加法的运算律
对任意
,有
(1)交换律:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe82a3f7f76832113ecf0e00803a589.png)
____________ .(2)结合律:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390c1ba83a744d73b4d39bae0eb076d8.png)
___________ .
对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd5f271e53d87d6286ca314bd52d440.png)
(1)交换律:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe82a3f7f76832113ecf0e00803a589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390c1ba83a744d73b4d39bae0eb076d8.png)
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