23-24高一下·全国·课前预习
1 . 请将复数集、实数集、虚数集、纯虚数集之间的关系用下图表示,并填在合适的空间.
您最近一年使用:0次
2 . 复数的定义
我们把形如
的数叫做复数,其中i叫做_________ ,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bef5a75ca975c523f7233f7a7585f4.png)
_________ .
我们把形如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77df5eaef09da6f7c46b4ab5e1ffe92b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bef5a75ca975c523f7233f7a7585f4.png)
您最近一年使用:0次
23-24高一下·全国·课前预习
3 . 复数通常用字母z表示,即
,其中的a与b分别叫做复数z的______ 与________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbff022b87295c5aa3a81894661f0bf0.png)
您最近一年使用:0次
23-24高一下·全国·课前预习
4 . 对于复数
, 复数
,
为实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39c662a3927de39135c3eee4b9cb68f.png)
__________ ;
为虚数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39c662a3927de39135c3eee4b9cb68f.png)
__________ ;
为纯虚数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39c662a3927de39135c3eee4b9cb68f.png)
__________ ;
为非纯虚数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39c662a3927de39135c3eee4b9cb68f.png)
__________ .
即复数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbff022b87295c5aa3a81894661f0bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbff022b87295c5aa3a81894661f0bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbff022b87295c5aa3a81894661f0bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39c662a3927de39135c3eee4b9cb68f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39c662a3927de39135c3eee4b9cb68f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39c662a3927de39135c3eee4b9cb68f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39c662a3927de39135c3eee4b9cb68f.png)
即复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbff022b87295c5aa3a81894661f0bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4438414f3c7c9694128f5a4a5ab672e.png)
您最近一年使用:0次
23-24高一下·全国·课前预习
5 . 在复数集
中任取两个数
,
,规定
与
相等当且仅当____________ ,即复数相等:
⇔______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6cef8cac4bc6a00c4c0e6fbd99bf30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eed3d568acf369a315c7ab41c081049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39f8634e9eccb84bce5dd266a241909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eed3d568acf369a315c7ab41c081049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87e591b738d9cda5084e5743354a514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4063994562bb3788c4999b82ff82b3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c822de0f8922c0cfef29e76d24fb19.png)
您最近一年使用:0次
23-24高一下·全国·课前预习
6 . 复数集
全体复数所构成的集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8030bb28d45a7fbf9fbf03730c654146.png)
__________ 叫做复数集.
全体复数所构成的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8030bb28d45a7fbf9fbf03730c654146.png)
您最近一年使用:0次
23-24高一下·全国·课前预习
7 . 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 | ![]() |
您最近一年使用:0次
23-24高一下·全国·课前预习
8 . 计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f552e9a55454b59d85161f57d6ff24.png)
您最近一年使用:0次
23-24高一下·全国·课堂例题
9 . 写出下列复数对应的向量:
,
,
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ccfc8f518104f35f29380e47dd3d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9845fcf800c01a35d37bf592b66755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44c492cd91061c6aa112093430ab36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
您最近一年使用:0次
23-24高一下·全国·课后作业
解题方法
10 . 已知复数
(i为虚数单位),求适合下列条件的实数m的值;
(1)z为实数;
(2)z为虚数;
(3)z为纯虚数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83209249416415be493d996f1f56de9d.png)
(1)z为实数;
(2)z为虚数;
(3)z为纯虚数.
您最近一年使用:0次