1 . 设z是虚数,在平面直角坐标系xOy中,z,
,
对应的向量分别为
,
,
.
(1)证明:O,B,C三点共线;
(2)若
,求向量
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1245ed74a632317d3a0a106aa9d02eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
(1)证明:O,B,C三点共线;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877f1a7e02a675480afc50d144782c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e973a6cfc29bbeade6d6654d286b5c22.png)
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解题方法
2 . 已知复数
(
,
),若存在实数
使得
成立.
(1)求证:
为定值;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c65960ea0efb14be3da6e949fde93b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754826457671db8939098215943e656a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d0adee5959236f30abeea5f68a41e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
您最近一年使用:0次
3 . 莱昂哈德·欧拉
,瑞士数学家、自然科学家.
岁时入读巴塞尔大学,
岁大学毕业,
岁获得硕士学位,他是数学史上最多产的数学家.其中之一就是他发现并证明欧拉公式
,从而建立了三角函数和指数函数的关系.若将其中的
取作
就得到了欧拉恒等式
,它是数学里令人着迷的一个公式,它将数学里最重要的几个量联系起来:两个超越数:自然对数的底数
,圆周率
;两个单位:虚数单位
和自然数单位
;以及被称为人类伟大发现之一的
,数学家评价它是“上帝创造的公式”请你根据欧拉公式:
,解决以下问题:
(1)试将复数
写成
(
、
,
是虚数单位)的形式;
(2)试求复数
的模.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec5ddb7c9c4540ac698b0386901af15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d70c067339e0c34782459c774c50a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1c64f68dd466b47b91550fb1dfca34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d70c067339e0c34782459c774c50a3.png)
(1)试将复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df53eed79f4f0a3bd4a088ff81cac40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc228995efbba2e64d7f1de747024cc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
(2)试求复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdbfce71f2f2e791d324226f359b2c3.png)
您最近一年使用:0次
2020-03-26更新
|
392次组卷
|
2卷引用:江苏省南京市秦淮中学2019-2020学年高二(美术班)上学期期末数学试题