名校
1 . 已知
为虚数单位,复数
满足
.
(1)若
,求复数
的辐角主值;
(2)若
,复数
满足
为实数.则复数
在复平面上所对应的点的集合是什么图形?说明理由.
(3)已知复平面上点
对应的复数分别为
.记复数
的辐角主值为
.求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a491320664d2f5bab356117541b83347.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1089162a06a53efac3a30f60f4e3b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cad1818490526d558c914a1938becc1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619adeb9313fcd751282961292d59854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7408c9a6328cc085608bbcfd9cce4e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(3)已知复平面上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c851465a30dd28567031e4773cd5deb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f638c4517048807bfbc3d82044b370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
您最近一年使用:0次
2 . 对于非空集合
,定义其在某一运算(统称乘法)“×”下的代数结构称为“群”
,简记为
.而判断
是否为一个群,需验证以下三点:
1.(封闭性)对于规定的“×”运算,对任意
,都须满足
;
2.(结合律)对于规定的“×”运算,对任意
,都须满足
;
3.(恒等元)存在
,使得对任意
,
;
4.(逆的存在性)对任意
,都存在
,使得
.
记群
所含的元素个数为
,则群
也称作“
阶群”.若群
的“×”运算满足交换律,即对任意
,
,我们称
为一个阿贝尔群(或交换群).
(1)证明:所有实数在普通加法运算下构成群
;
(2)记
为所有模长为1的复数构成的集合,请找出一个合适的“×”运算使得
在该运算下构成一个群
,并说明理由;
(3)所有阶数小于等于四的群
是否都是阿贝尔群?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38bdb8d4c486c37ac64517ed8d60888b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1240721fdf6d8e1ed9c1158ae723637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
1.(封闭性)对于规定的“×”运算,对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9cbad1e8b405feac6e8fe403f024b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830afd1befcf1a92874b5e0bc214578d.png)
2.(结合律)对于规定的“×”运算,对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d4ef2c168b3dba086f2485c3c9cc7c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d2d88c195317bf5827a1304068f26a.png)
3.(恒等元)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e6faeeed98a19d7012c921ca71a046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572f76c63e3a74a90a1e6ca5ae401cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e4c22a6a498e197149ce29d9e98fce.png)
4.(逆的存在性)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572f76c63e3a74a90a1e6ca5ae401cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5463eaf01a62bc6a772301d9e2ad19c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1487cef1d4227621d9311541dec87156.png)
记群
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f2eb65f2fe6546a5e318343d25fe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f2eb65f2fe6546a5e318343d25fe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d22c891ccf3768b616c5ddaad575aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c679fe86736064c65a292db59cb739c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
(1)证明:所有实数在普通加法运算下构成群
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74ba4c1c25324a8875b09d0c855a82ad.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d719c0c82f38a886db86c71bbaf8db32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d719c0c82f38a886db86c71bbaf8db32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4ef5fbf807246591e03d07ba4e3a4e.png)
(3)所有阶数小于等于四的群
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
您最近一年使用:0次
3 . 对于函数
,分别在
处作函数
的切线,记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”,同理记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”
(1)设函数
,记
“切线-
轴数列”为
,记
为
的前n项和,求
.
(2)设函数
,记
“切线-
轴数列”为
,猜想
的通项公式并证明你的结论.
(3)设复数
均为不为0的实数,记
为
的共轭复数,设
,记
“切线-
轴数列”为
,求证:对于任意的不为0的实数
,总有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ed953d6e0bd80a5da66552c7bfbcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3d48fa9493a86f262569df235a82ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8292395dc894796602a60486e575a808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ef5756fec38d1b4dc62358b45c3352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e845964df4b271bd7b4cf99ede79be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bcf306a6aa8554d1d7fc8317f4e946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5f303f666e164582da05968d9d8cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6f044a9b06a7a769e613c977cbfb87.png)
您最近一年使用:0次
2024-01-01更新
|
441次组卷
|
7卷引用:上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题
上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题(已下线)模块一专题1【练】《导数的概念、运算及其几何意义》单元检测篇B提升卷(人教A2019版)(已下线)模块二 专题1 与曲线的切线相关问题(已下线)模块二 专题3 与曲线的切线相关问题(人教B版)(已下线)模块一 专题1 《导数的概念、运算及其几何意义》B提升卷(苏教版)(已下线)模块二 专题1 与曲线的切线相关问题(苏教版高二)(已下线)模块二 专题4 与曲线的切线相关问题(高二北师大版)
4 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5d2ccba293fac59443cf6f0cd3c408.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5d2ccba293fac59443cf6f0cd3c408.png)
您最近一年使用:0次
5 . 通过平面直角坐标系,我们可以用有序实数对表示向量.类似的,我们可以把有序复数对
看作一个向量,记
,则称
为复向量.类比平面向量的相关运算法则,对于
,
,
、
、
、
、
,我们有如下运算法则:
①
; ②
;
③
; ④
.
(1)设
,
,求
和
.
(2)由平面向量的数量积满足的运算律,我们类比得到复向量的相关结论:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb72256695bffefefffc1572fc08f45.png)
②
③
.
试判断这三个结论是否正确,并对正确的结论予以证明.
(3)若
,集合
,
.对于任意的
,求出满足条件
的
,并将此时的
记为
,证明对任意的
,不等式
恒成立.
根据对上述问题的解答过程,试写出一个一般性的命题(不需要证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbee4027127a0bce1cdc3fc50d28c5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1d1ef701f3618fa1884a3791d366aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1d1ef701f3618fa1884a3791d366aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa0a749b475d60688fac80c38156eea.png)
![](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/d7def0e6fc765f99565eaa1d498e291c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaaebd6ed5e92ec8986cbe043ab574ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8ba665154ad6f7ccb8ca422837e7c.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd637dcc0c2703912c91ad32bbd7dc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc6b415aea966f160e3f3085cef1f6e.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad6cc9ce836150c84f3c7b354e15057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b017a79eadd64416f98c7acb0f5bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd8bbf47b69bbd7a6263b041290d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39d1d88189726ae99c309644fca3494.png)
(2)由平面向量的数量积满足的运算律,我们类比得到复向量的相关结论:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb72256695bffefefffc1572fc08f45.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b55031cf0985ff92dd0c16f1ad4d01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7e78abccf1d9228fdf68e7ecf58465.png)
试判断这三个结论是否正确,并对正确的结论予以证明.
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f943fd00c91acee53d2e9f4b31a5437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8ed19b9d61c48d77a9fc37335f47f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1e98efe26c2c1442f6a73f09ec8d01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40891013fa6a2a7ccee812efe7643e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b6dbee41d492940e58103a9aaa2e7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b452962126ea36badc6354f5e2b1d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1e98efe26c2c1442f6a73f09ec8d01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ab37842e5e918ff46a4089e234d04b.png)
根据对上述问题的解答过程,试写出一个一般性的命题(不需要证明).
您最近一年使用:0次
2023-07-06更新
|
553次组卷
|
7卷引用:上海市闵行区2022-2023学年高一下学期期末数学试题
上海市闵行区2022-2023学年高一下学期期末数学试题(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)(已下线)专题01 复数-《期末真题分类汇编》(上海专用)(已下线)专题7.4 复数运算的综合应用大题专项训练-举一反三系列-(已下线)第06讲 第七章 复数 章节验收测评卷-【帮课堂】(人教A版2019必修第二册)(已下线)第12章 复数单元综合能力测试卷-【帮课堂】(苏教版2019必修第二册)(已下线)专题03 复数-《期末真题分类汇编》(人教A版2019必修第二册)
名校
6 . 设
是一个关于复数z的表达式,若
(其中x,y,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b1cee5ac65b4e32cb0fb9e5ba4da6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
为虚数单位),就称f将点
“f对应”到点
.例如
将点
“f对应”到点
.
(1)若
点
“f对应”到点
,点
“f对应”到点
,求点
、
的坐标;
(2)设常数
,
,若直线l:
,
,是否存在一个有序实数对
,使得直线l上的任意一点
“对应”到点
后,点Q仍在直线
上?若存在,试求出所有的有序实数对
;若不存在,请说明理由;
(3)设常数
,
,集合
且
和
且
,若
满足:①对于集合D中的任意一个元素z,都有
;②对于集合A中的任意一个元素
,都存在集合D中的元素z使得
.请写出满足条件的一个有序实数对
,并论证此时的
满足条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c01e03a93ade8659780af659f12e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5bbd08209bda97df3e33163556561e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b1cee5ac65b4e32cb0fb9e5ba4da6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30096b7bfb7d8e94336df5d1f92f16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969b9043717a5b07402958abc5749290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef66a0582e95fb5c57a405acdea9a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b40590fd0945eb5c688d64e0a8d9f3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f669a1d6376f795f05b47eb7d8067c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2692896964f98fc258f795c0be6dd35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(2)设常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96f5020aef5aef03ec7f406460f608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649546dd164eaac1f5f77a20293899c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b9dfb28a818d4435d04c101174bbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30096b7bfb7d8e94336df5d1f92f16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b9dfb28a818d4435d04c101174bbbb.png)
(3)设常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c471126f22232a1ff1e88591bde0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3473c334445af65176dde2d2e5d890ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0054d6123e214792c699c3ec1a1f8fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9f9cebf7c3111773f43f0be6510148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3ac8e9f3746c0993b1f1d31620fec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70b34fa2acd6a5c2e2e37222d58ec68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2527414d896f7af69a7a620e1cc57676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c01e03a93ade8659780af659f12e09.png)
您最近一年使用:0次
2023-07-05更新
|
990次组卷
|
9卷引用:上海市控江中学2022-2023学年高一下学期期末数学试题
上海市控江中学2022-2023学年高一下学期期末数学试题上海市静安区回民中学2024届高三上学期12月阶段性测试数学试题(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)(已下线)专题01 条件开放型【练】【通用版】湖南省邵阳市第二中学2024届高三下学期入学测试数学试题(已下线)高一下学期期中数学试卷(提高篇)-举一反三系列浙江省绍兴市第一中学2023-2024学年高一平行班下学期期中考试数学试卷(已下线)专题03 复数-《期末真题分类汇编》(人教A版2019必修第二册)江苏省泰兴中学、泰州中学2023-2024学年高一下学期5月联合质量检测数学试卷
名校
解题方法
7 .
被称为欧拉公式.我们运用欧拉公式,可以推导出倍角公式.如:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4511b4a678755f69f4a9a82b117cca3c.png)
.类比方法,我们可以得到![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c87e34f4681791e0a5d00fd70576030.png)
____ (用含有
的式子表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc0ab4d45a4bef21ba8ae793f2e76f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4511b4a678755f69f4a9a82b117cca3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ef5b2ea33b6ea08df130ce079aac19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c87e34f4681791e0a5d00fd70576030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48345d239aaf8e9ca1ff2846c08a99.png)
您最近一年使用:0次
8 . 设非零复数
满足关系
,且
的实部为
,其中
.
(1)当
时,求复数
,使
在复平面上对应的点位于实轴的下方;
(2)是否存在正整数
,使得
对于任意实数
,只有最小值而无最大值?若存在这样的
的值,请求出此时使
取得最小值的
的值;若不存在这样的
的值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f1634127d28d75188bbd14f18ed4d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032dda7c614a24a0c9b484da313fb999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e8694471e5f29fc1c5e0d5413244be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4958020c09be9a6dc5d789a86a25a09.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8176754726d2194c890e80df1a1f1c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978a4be6428044bef22c0a4c6ba0ec50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
9 . 已知函数
,其中
,证明:存在
,且
.
的根的实部全部大于0.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b748237d3ad510f872cb96097e0e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f016c950ab496393ba95c709cbc6e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0e0c37d5595299c1886e6d812a946e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3ac8c6973c1a97dc47d4fb6737c709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7165f4d49fc207e7cdc35fccdb18e532.png)
您最近一年使用:0次
名校
解题方法
10 . 已知
(
为虚数单位).设集合
,则集合
中的元素在复平面上对应点所形成图形的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3a7e1ea06b2eb0061ad24605eb7fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02822aa4caeab52a3b2e8d9dba18d74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次