23-24高一下·全国·课前预习
1 . 两个复数相乘时,如图所示,先画出与
对应的向量
,
,然后把向量
绕点
按_____ 时针方向旋转角
,(如果
,就要把
绕点
按_____ 时针方向旋转
),再把它的模变为原来的____ 倍,得到向量
,
表示的复数就是积_____ ,这是复数乘法的几何意义.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30deb1f343048675b9b231620369668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1640d3fff861f45c5eb4019943b000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30deb1f343048675b9b231620369668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d442c6f979cd09bb7f8acf01d70130fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30deb1f343048675b9b231620369668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba62723e05ce6cce4d089d8b201fa857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb0e25bbccbee4a1b9db38b49e87978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb0e25bbccbee4a1b9db38b49e87978.png)
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23-24高一下·全国·课前预习
2 . 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.
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23-24高一下·全国·课前预习
3 . 设
的三角形式分别是
,
那么,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e13b9c2f224325b25b10a9235bc8d2.png)
________________ =_________________ .
这就是说,两个复数相乘,积的模等于各复数的模的积,积的辐角等于各复数的辐角的和.简记为:模相乘,辐角相加.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dccba71c515f43296221e5291354b8cb.png)
那么,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e13b9c2f224325b25b10a9235bc8d2.png)
这就是说,两个复数相乘,积的模等于各复数的模的积,积的辐角等于各复数的辐角的和.简记为:模相乘,辐角相加.
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23-24高一下·全国·课前预习
4 . 我们规定在_________ 范围内的辐角的值为________ ,通常记作
,即
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f56cfb41ee7cb758fee138ab09e0d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e0efe34fcd26951f58ef4eecaf697a.png)
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23-24高一下·全国·课前预习
5 . 对于复数0,因为它对应着零向量,而零向量的方向是任意的,所以复数的辐角也是______ .
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23-24高一下·全国·课前预习
6 . 任何一个不为零的复数的辐角有无限个值,且这些值相差_____ 的整数倍.
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7 . 一般地,任何一个复数
都可以表示成
的形式,其中,_____ 是复数的模;
是以
轴的非负半轴为始边,向量
所在射线(射线
)为终边的角,叫做复数
的_____ ,
叫复数的三角表示式,简称三角形式.为了与三角形式分开来,
叫做复数的代数表示式,简称代数形式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f543c26ef2de07fb132ba386a8b498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6b88af810dbab3e7a0e9baeafb15f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb0e25bbccbee4a1b9db38b49e87978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54d290009e138d1f0d4cb771cada9f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6b88af810dbab3e7a0e9baeafb15f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
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8 . 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)
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23-24高一下·全国·课前预习
9 . 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)
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