23-24高一下·全国·课前预习
1 . 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
2 . 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
3 . 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
4 . 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
5 . 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
6 . 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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21-22高一·全国·课后作业
7 . 复数
的值为( )
A.
B.
C.
D.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc317ef7b5ee9ef35b24b7884f22c31.png)
A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1459c084d7a4f2481ca5bc1aeadb990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618cad551b468991285ebc817fa8ddd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3240d159eca3bf4ba82d969e9d4451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b1b2ca0fee8cd5fc657e5ae7efd9f4.png)
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