1 . 计算:
(1)
;
(2)
;
(3)
的立方根;
(4)
的6次方根;
(5)
的6次方根.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2624a8fc7d36c684778b15ea7aa9da7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e90bfc366569bf737f8e0a124f753af.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcee1e29795720fa2c8422e577959841.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0903c99c792c88caf2d82c0bba47c6db.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb075ac02eed900dd62494c016094a2.png)
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2 . 对一般的实系数一元三次方程
,由于总可以通过代换
消去其二次项,就可以变为方程
.在一些数学工具书中,我们可以找到方程
的求根公式,这一公式被称为卡尔丹公式,它是以16世纪意大利数学家卡尔丹(J.Cardan)的名字命名的.
卡尔丹公式的获得过程如下:三次方程
可以变形为
,把未知数x写成两数之和
,再把等式
的右边展开,就得到
,即
.将上式与
相对照,得到
,把此方程组中的第一个方程两边同时作三次方,
,并把
与
看成未知数,解得
,于是,方程
一个根可以写成
.
阅读以上材料,求解方程
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eccb3856fa5aa8dc822a593ec88ca2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0f3c81f415857813838d4b9b714d56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5dd275a6062b21f9c3e9155c7e0ba62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5dd275a6062b21f9c3e9155c7e0ba62.png)
卡尔丹公式的获得过程如下:三次方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5dd275a6062b21f9c3e9155c7e0ba62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ead1b77b69e6b51d6d483331fd01d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bed1a02239821a616bc173181e7ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c26aacdd3362aa65b2966045cbfcddf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f02c3aa1326c9b1e069b6997cd29bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11792ad247341c0dbc80663dd0fa6f77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ead1b77b69e6b51d6d483331fd01d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a28d84fa30daeb6cfcb0347d1d40a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718a7346b05d9a0c4f31a60d8786404b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36accab23dbd172687769aea43e5781c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411a315870ed3e6d0e8ea885f1a04bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b79aba80a3fc337b27ed567abf1e5c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5dd275a6062b21f9c3e9155c7e0ba62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d63387694fd1caafce80adfb43c86b.png)
阅读以上材料,求解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c3d494147195cf4f5e1fa3f6f5a0b9.png)
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3 . 求满足下列各条件的复数
.
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b349ace2eb4ebface37f0ad63b5f0d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e9547bc43deeacb3266155dc81f48b.png)
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21-22高一·湖南·课后作业
4 . 解方程:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6387baa65c2117aae2e3c96195a423.png)
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解题方法
5 . 设复数
,a为实数,
.若z是方程
的一个根,且z在复平面上对应的点在第一象限,求
与a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f892fed33a4203b65c36ea5a5cfd24dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef001eeef468ca21ac0cbb23fd135657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fc19c302085de8a90e2827c32f15e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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6 . 在复数集C内解下列方程:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406f2e4d002383ebbfadb704292b020d.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac906f8edd88001541fb91289a9ab95.png)
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88fe8459a4eb70d4ade190868adac94.png)
(4)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406f2e4d002383ebbfadb704292b020d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac906f8edd88001541fb91289a9ab95.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88fe8459a4eb70d4ade190868adac94.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612754452b05e055bc400dd4947ea325.png)
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名校
7 . 关于x的方程
的两个根为
.
(1)若
,求实数m的值;
(2)若
,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd63ba63460f33274ed478ab83b6efc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585acb8d9fd80c6a8e456b997a71eb44.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c9448df33ed1b7fdaefe2b5b199caa5.png)
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2021-11-10更新
|
413次组卷
|
3卷引用:专题5.1 复数的四则运算-2021-2022学年高一数学北师大版2019必修第二册
8 .
是实系数一元二次方程
的两个虚根,且
是实数,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fa32c1e926f40a0722d106563777ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189222885ebe0400731be0bd0fe72ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
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9 . 已知关于
的方程
(
)的两根为
,且
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a70607e379c14fee81f21f3576678c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc14778010a33f90902ff17b1ec0ac73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd2773114a2b61601c96be079210a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-12-03更新
|
1126次组卷
|
4卷引用:沪教版(2020) 必修第二册 高效课堂 第九章 复数 9.3 实系数一元二次方程(2)
沪教版(2020) 必修第二册 高效课堂 第九章 复数 9.3 实系数一元二次方程(2)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上海市理工大附中2018-2019学年高二下学期期末数学试题(已下线)专题4.3 复数【压轴题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)
13-14高二下·江苏无锡·期中
解题方法
10 . 已知复数
,
,
为纯虚数.
(1)求实数
的值;
(2)求复数
的平方根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0bebff50e9705cc278900dde2e6568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5968b758a791e35fc86d33f9783ed0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
您最近一年使用:0次
2016-12-03更新
|
1636次组卷
|
4卷引用:第五章 复数章末检测卷-2021-2022学年高一下学期数学北师大版(2019)必修第二册
第五章 复数章末检测卷-2021-2022学年高一下学期数学北师大版(2019)必修第二册(已下线)2013-2014学年江苏无锡洛社高级中学高二下学期期中考试理科数学卷(已下线)2013-2014学年江苏无锡洛社高级中学高二下学期期中考试文科数学卷江苏省江阴市四校2016-2017学年高二下学期期中考试数学(理)试题