名校
1 . (1)计算:的值;
(2)在复数范围内解关于的方程:
;
(3)设复数,
满足
,
,求
的值.
您最近一年使用:0次
解题方法
2 . 1799年,哥廷根大学的高斯在其博士论文中证明了如下定理:任何复系数一元
次多项式方程在复数域上至少有一根(
).此定理被称为代数基本定理,在代数乃至整个数学中起着基础作用.由此定理还可以推出以下重要结论:
次复系数多项式方程在复数域内有且只有
个根(重根按重数计算).对于
次复系数多项式
,其中
,
,
,若方程
有
个复根
,则有如下的高阶韦达定理:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68be203b2490ecce4c0e2eadeb5d911b.png)
(1)在复数域内解方程
;
(2)若三次方程
的三个根分别是
,
,
(
为虚数单位),求
,
,
的值;
(3)在
的多项式
中,已知
,
,
,
为非零实数,且方程
的根恰好全是正实数,求出该方程的所有根(用含
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b024d78f428194127b5534f948810def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7230de53663c75658c58bbf206a0085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bed25da42194b5a81d123933d5704f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3759b3561834cdc5b499b91f3850d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83590c4a7ea5636843dd4b60c67cb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68be203b2490ecce4c0e2eadeb5d911b.png)
(1)在复数域内解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4800c5aa0e5b70b2141541cbd3853e34.png)
(2)若三次方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac603c0b3d1d7fd42bd50222b6ab94d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6755cd39b121a0dd2a14da8d43c1fff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ddb97874a62bb5530514a467d64af13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8079c5a2d8674d322f7abe6d4ef4a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.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)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b024d78f428194127b5534f948810def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb3db0a99f86232e0cf3e55c789ea99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2e2674707c28eddd3f3ab60f73f54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c37d6353f394a5704a92113908a5c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
3 . 已知
是复数,
与
均为实数.
(1)求
;
(2)若复数
是方程
的一个解,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/005f6a19fe7b2709a8447830ea0a024a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c32849bfd957f6f3bba6f29dfefc388.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ea3cc01ce7266cdf0fd73fd50d23c8.png)
(2)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae9ab71d1179a20680652f8c68e77c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72850427e83ff19a24305783e080b280.png)
您最近一年使用:0次
2024-05-09更新
|
388次组卷
|
3卷引用:福建省泉州第五中学2023-2024学年高一下学期期中考试数学试题
福建省泉州第五中学2023-2024学年高一下学期期中考试数学试题(已下线)专题06 复数-期末考点大串讲(人教B版2019必修第四册)江苏省宿迁市泗阳县两校联考2023-2024学年高一下学期第二次学情调研(5月月考)数学试题
名校
解题方法
4 . 已知复数
、
是方程
的解.
(1)
的值;
(2)若复平面内表示
的点在第三象限,
为纯虚数,其中
,求
的值.
![](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/f2d7dc3fa43ef2ed97945ce21a208d42.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e487d5357e01ee9df8526cd0f37a8b.png)
(2)若复平面内表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3893f025b225f22f5fb6f8ea71aa9c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-07-28更新
|
353次组卷
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4卷引用:FHsx1225yl191
(已下线)FHsx1225yl191(已下线)【高一模块二】类型3 以复数为背景的解答题(B卷提升卷)山东省临沂市罗庄区2022-2023学年高一下学期期中数学试题江西省萍乡市安源中学2022-2023学年高一下学期期末质量检测数学试题
解题方法
5 . 已知复数是方程
的解,
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13997a98685e66487800de874015cbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd1cf228141f1668f0f2015e534178a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff0f1b6dd0be54207299f6c22eec25f.png)
您最近一年使用:0次
2023-03-02更新
|
562次组卷
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5卷引用:7.2.2复数的乘、除运算(第2课时)
(已下线)7.2.2复数的乘、除运算(第2课时)上海市民办丰华高级中学2021-2022学年高一下学期期末数学试题(已下线)专题强化 复数高频考点一遍过精练必刷题-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(苏教版2019必修第二册)浙江省温州新力量联盟2022-2023学年高一下学期期中联考数学试题(已下线)核心考点02复数(2)