解题方法
1 . 已知集合
(其中
是虚数单位)
,定义:
,
.
(1)计算
的值;
(2)记
,若
,且满足
,求
的最大值,并写出一组符合题意的
、
;
(3)若
,且满足
,
,记
,求证:当
时,函数
必存在唯一的零点
,且当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531f55c9de4647282bc0424a81f4fd25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ddb621d78a738eba6ebafecbbd7d06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47aa3fcf666d1169ceca5e1e720b926e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ccc73232efc9d641adcbae21035944.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0ff8b406a295a58f4fbb36b4c292fa.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be674fcbd2fd1a608fd4a9705c70db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e7c6170cd75c5a40d7e695eda15e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e95d018246b699601d127e79ec46131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f82089a3186fdffaa2535faebd3d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b54286fe72b8305272c36c0a3a8d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f7d480cfc89b872404666083e62db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546ababc482b51df95c4aba05ee18c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d828db2a08e2a1da164a0012cc6627a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661249bf6499017f9e5e03db3fcd93d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d5ec74c81f7d02f273f7eecefaf9a7.png)
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2 . 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)
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名校
解题方法
3 . 设复数
,其在复平面内对应点为
,且
,复数
,其在复平面内对应点为
,且
,若存在
的轨迹上的两点
、
,使
,则
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f41acaa456df1ac6e5af4fc056f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c69a18ac82d772e7c7707efe8f44eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72aeab648917f787ddb15d9039b8856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e380c51ad6d645900156ff061992799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42143191548a417aa602e2f884df244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 复数除了代数形式
之外,还有两种形式,分别是三角形式和指数形式,著名的欧拉公式
体现了两种形式之间的联系.利用复数的三角形式进行乘法运算,我们可以定义旋转变换.根据
,我们定义:在直角坐标系内,将任一点绕原点逆时针方向旋转
的变换称为旋转角是
的旋转变换.设点
经过旋转角是
的旋转变换下得到的点为
,且旋转变换的表达式为
曲线的旋转变换也如此,比如将“对勾”函数
图象上每一点绕原点逆时针旋转
后就得到双曲线:
.
(1)求点
在旋转角是
的旋转变化下得到的点的坐标;
(2)求曲线
在旋转角是
的旋转变化下所得到的曲线方程;
(3)等边
中,
在曲线
上,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eed3d568acf369a315c7ab41c081049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26032c72018539ca7aa3ca66ac845260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224921c5f4e35b546b1fa8b65323086b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c65d3d6119b18fd2427497cbd413c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e92cb090fd6e4ce2779ddb11ec365c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d06619274d7c0e540c0e7dbbdbbfbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e24f048f9a87274863ba2c037d7a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a93855bd1b93f92a6b41da629d6f9d.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f6fb134624fa01a9b3eb651434944d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
(3)等边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894eb4285cb70b66fe2b60a36d07f3ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
5 . 现定义“
维形态复数
”:
,其中
为虚数单位,
,
.
(1)当
时,证明:“2维形态复数”与“1维形态复数”之间存在平方关系;
(2)若“2维形态复数”与“3维形态复数”相等,求
的值;
(3)若正整数
,
,满足
,
,证明:存在有理数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9d830212489b316bb052455098108e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc8299790d98621b87e73212a2ebb91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905dd10639c9fef5ef8d66a124756140.png)
(2)若“2维形态复数”与“3维形态复数”相等,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c136aaf9b5dedec254a92ce302f4a70c.png)
(3)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94742ebbb028c50d7a58e3e8f4ab329c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35490c12e57ecd91af9934cb17b5c927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed110fbfeb14003270a1039ba174d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f02f2606180ffeda602ff9ae747af6f.png)
您最近一年使用:0次
2024-05-11更新
|
742次组卷
|
4卷引用:安徽省合肥市第一中学2023-2024学年高一下学期5月期中联考数学试题
名校
6 . 我们知道复数有三角形式,
,其中
为复数的模,
为辐角主值.由复数的三角形式可得出,若
,
,则
.其几何意义是把向量
绕点
按逆时针方向旋转角
(如果
,就要把
绕点
按顺时针方向旋转角
),再把它的模变为原来的
倍.
已知圆
半径为1,圆
的内接正方形
的四个顶点均在圆
上运动,建立如图所示坐标系,设
点所对应的复数为
,
点所对应的复数为
,
点所对应的复数为
,
点所对应的复数为
.
,求出
,
;
(2)如图,若
,以
为边作等边
,且
在
上方.
(ⅰ)求线段
长度的最小值;
(ⅱ)若
(
,
),求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8865c033cf9f1652c22297f8669623a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5ff0388004b8b37c9eeaef46a27325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5e350620ff7aab6fefc18b88573c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9979e52e407b34b82c2f7a6788743feb.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/b1cd5637ee5adad7e0376422ed181edf.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/2b3e95410f3b4fcb0cba425b521d1f67.png)
已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b29a77cfdb8d2a0b684389921e1496c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2120c2838188e2affa317160f24251f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
(2)如图,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96499747e4aea990f4b878eea8d73ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499b1f470978c4f8cc05ffdebc2e961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
(ⅰ)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895928688d7557d94ccafa7ad073edfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2357ed8dbe6d3911738b8f747d670d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
您最近一年使用:0次
2024-05-04更新
|
617次组卷
|
3卷引用:重庆市南开中学校2023-2024学年高一下学期期中考试数学试题
重庆市南开中学校2023-2024学年高一下学期期中考试数学试题(已下线)5.3复数的三角形式-【帮课堂】(北师大版2019必修第二册)贵州省毕节市赫章县乌蒙山学校教育集团2023-2024学年高一下学期5月联考数学试题
名校
7 . 在复平面内的三个点
,
,
对应的复数分别是
,
,
,动点
对应复数
.若实数
,
满足
,且
,则
最大值为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395e44f474af7c750731115aa33d8860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce66396cc53ea6d566a4c16a485883d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734c5f0ab3f244ae2ce1ba7b618cb0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af329f493fc1677e963d59f60fe9f18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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解题方法
8 . 记复数的一个构造:从数集
中随机取出2个不同的数作为复数的实部和虚部.重复
次这样的构造,可得到
个复数,将它们的乘积记为
.已知复数具有运算性质:
,其中
.
(1)当
时,记
的取值为
,求
的分布列;
(2)当
时,求满足
的概率;
(3)求
的概率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57640b1fd3198b4923c61a7c5fb53c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6772d33e3e6b46834bfa6710d31d2f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e9c3910f721303685d56a8aeaccec2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080bca5fd0f1ac5d834074b3e00f92bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf2903ee65254ac0df06c3171cfec4f.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da7a625440c113848a5d7ad526d153c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
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名校
解题方法
9 . 复数是由意大利米兰学者卡当在十六世纪首次引入,经过达朗贝尔、棣莫弗、欧拉、高斯等人的工作,此概念逐渐为数学家所接受.形如
的数称为复数,其中
称为实部,
称为虚部,i称为虚数单位,
.当
时,
为实数;当
且时,
为纯虚数.其中
,叫做复数
的模.设
,
,
,
,
,
,
如图,点
,复数
可用点
表示,这个建立了直角坐标系来表示复数的平面叫做复平面,
轴叫做实轴,
轴叫做虚轴.显然,实轴上的点都表示实数;除了原点外,虚轴上的点都表示纯虚数.按照这种表示方法,每一个复数,有复平面内唯一的一个点和它对应,反过来,复平面内的每一个点,有唯一的一个复数和它对应.一般地,任何一个复数
都可以表示成
的形式,即
,其中
为复数
的模,
叫做复数
的辐角,我们规定
范围内的辐角
的值为辐角的主值,记作
.
叫做复数
的三角形式.
,
,求
、
的三角形式;
(2)设复数
,
,其中
,求
;
(3)在
中,已知
、
、
为三个内角
的对应边.借助平面直角坐标系及阅读材料中所给复数相关内容,证明:
①
;
②
,
,
.
注意:使用复数以外的方法证明不给分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c0c72c17b74f9a5a175ec2b9d77e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c789a7cd7ac2b8b96dc879c6c8161ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b011f69dfc5262a3d82f64676739b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fe68ea0bf368925909606949da47f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0bf9b2a7378e73e9fd06c693bfda07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368f9e12546277731776041c73dbe58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e80e5baee553150c67a91f1017a7be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6958203312cbda12fd2683a819dd9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e472aea001d179c284e3687a9aacf384.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e472aea001d179c284e3687a9aacf384.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/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec45476379fb51aa1ef0a93f849f48be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e283f3168c0b5e8f68dda92c43651e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eec3e684af41f9ed4db5b931b9ccfb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f56cfb41ee7cb758fee138ab09e0d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec45476379fb51aa1ef0a93f849f48be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3665b2dac544bfb2a0c175f95a480e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b3a15906b84b98a3ac563e7e2ec9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe615164ed2995bdeea0f5b0ba94231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
(2)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd87d6e1987cf95d102de1045d3722a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/398d8980d3ec9fbf536a1efa6312a19a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0492634f27279b6470798af0185be67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c723970ac738976e0130e1438b67058.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1501d4035822b34fcc2378f1e316f159.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63471f592531e46277365ed319e2acc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923694c299d953e02cb79dfcef9f56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ce2f54d69a5987c1de19da53342811.png)
注意:使用复数以外的方法证明不给分.
您最近一年使用:0次
2024-03-12更新
|
592次组卷
|
4卷引用:黑龙江省哈尔滨师范大学附属中学2023-2024学年高一下学期开学考试数学试卷
黑龙江省哈尔滨师范大学附属中学2023-2024学年高一下学期开学考试数学试卷重庆市缙云教育联盟2023-2024学年高一下学期3月月度质量检测数学试题(已下线)模块五 专题六 全真拔高模拟2(已下线)第七章:复数(新题型)-同步精品课堂(人教A版2019必修第二册)
10 . 对于无穷数列
,我们称
(规定
)为无穷数列
的指数型母函数.无穷数列1,1,…,1,…的指数型母函数记为
,它具有性质
.
(1)证明:
;
(2)记
.证明:
(其中i为虚数单位);
(3)以函数
为指数型母函数生成数列
,
.其中
称为伯努利数.证明:
.且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4003dc23cc843e98aa97220e8d3a84d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c9f9424671c7e1620be104f3defa49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a6580231b1438c017a656f0a0fcc35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f59e9a69ab35dc4eb89904ec903f7e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a5e730877d3a07af9a7fb11e12e3ce.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68dddd478b94b9c21a5575a76b1dd51b.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17cc30d1487ffbb3ae0dc8ad8cbd032f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4a45607fc2a2e2316896ebd034bd0e.png)
(3)以函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b425361a8411f7d5fafdb625548e10e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed900c88cf1ca707255cd73398f6321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadf60fd2b3e31a83cb7ce708190b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b3e125cdfc173e4ef5a60f6cdc026d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8bb98fa13c7ec31472fca5a33ac80.png)
您最近一年使用:0次
2024-03-03更新
|
574次组卷
|
3卷引用:安徽省蚌埠市2024届高三下学期第三次教学质量检查数学试题