23-24高一下·全国·随堂练习
1 . 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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解题方法
2 . (1)在复平面上画出与以下复数
,
,
,
分别对应的点
,
,
,
.
,
,
,
.
(2)求向量
,
,
,
的模.
(3)点
,
,
,
中是否存在两个点关于实轴对称?若存在,则它们所对应的复数有什么关系?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b29a77cfdb8d2a0b684389921e1496c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a976c188b072c749662aedf482193dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11988aa7569790689bea75a91925eeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0c37c074c1b18db19e9a315abe7815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a1508dfc7acb431d0ffc31e549e353.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96cb7ee166966ed0b1605c263e433cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc77d6da6e8f3ad5c239e7cc6c9930c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed22ce98b22693a90269d933bb6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a7cb1e5ee3fe9de342bb85371db7e5.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
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21-22高一·湖南·课后作业
3 . 已知复数
,
,
,
,
.
(2)求各复数的模;
(3)求各复数的共轭复数,并在复平面内作出这些共轭复数对应的向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8902c5c098f5f4787fcb0ca8f3e334c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae5fa3b1e6e2d7e7fa91ded783a41a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780033e15945059e5f0c108ac93fde11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb249662433aacbebc9acd3c7823061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8664f38793b7a1b9b5d0bf3c9e223a08.png)
(2)求各复数的模;
(3)求各复数的共轭复数,并在复平面内作出这些共轭复数对应的向量.
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20-21高一·全国·课后作业
4 . 已知复数
、
、
、
、
.
(1)在复平面内分别作出与这些复数对应的向量;
(2)分别写出这些复数的共轭复数,并求它们的模.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92bc544264689eb22a1548defc693901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4a8f8c20c8d876f4f002e6e5bb38d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354e37769f1ab1e481c5a826fbb7ceb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50078dac06366a98d4bc4d2c996412ee.png)
(1)在复平面内分别作出与这些复数对应的向量;
(2)分别写出这些复数的共轭复数,并求它们的模.
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