解题方法
1 . 复平面
与
交点个数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87432634f161e669f23527a5fc813ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70c2519610d6d1d6d0855b0f27dfc5e.png)
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2 . 若e为自然对数的底,则满足
,且
的复数z的个数为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ec0e75b252dde0973ef2efe32f9577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f92c6a49d8c173eb40188da78246103.png)
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3 . 设
,其中
为质数.对
的一个子集
,如果
中所有元素的和(空集的元素和规定为
)为
的倍数,则称
是
的一个“倍子集”.试求
的所有倍子集的个数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26e093e724f3c26f1eaf8db779bf2f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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4 . 若复数
满足
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dbebbc7b2d8677ad057247cd6b2c0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b626bfc67956dc3f13df12b53038e07.png)
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5 . 对于给定的角
,
,…,
,试讨论方程
是否有模大于2的复数根?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf9811e872dc8623fac91c19a19cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af20e1d74b2ed748457d1d9a8ee65e8.png)
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6 . 设
,其中
和
都是实数,且
.证明:若
,则对一切正整数
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f167a87f1dfceaf858d4dde6ee94ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3fb0c9c7e30bbc0ec8c3521577ee4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921c99563c54509e2ebf587dfdb26e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042235c88be02463c0b7bef603ae7e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58edc69cbf7d0d5d1ce8a1dc6c125af5.png)
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7 . 平面上给定
及点
,构造点列
,
,
,…,使得
为点
绕中心
顺时针旋转
时所到达的位置,而
和
为点
和
分别绕中心
和
顺时针旋转
时所到达的位置,
.若对某个
,有
,试求
的各个内角的度数及三个顶点
,
,
的排列方向.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff63b9623ec6dd0c67481553c3df09f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc0453cd2c10c3d4ea22f257901f69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ec847a264e4b9f9aa37ef642e53998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe639eab78eafd2d40ea70aa5d3f21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ba52b2310c4c86524386416df1dc16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2dca6c7b7b92de55adda9dc63e8ac78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5055f1871e5af43a405c4fb819d5026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ba52b2310c4c86524386416df1dc16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b975f35ecfc9641688e682bcee70e1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559cb3a8f84812f4eafb5c370999a02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbdf4cf37e577168788b46bfe642e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b58e436b5db279809f633d017f38c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
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8 . 设非零复数
满足
,则代数式
的值是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e48bdc43f37bb361303f6e8ffd2175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4947fd294688c7b53aa2124ca01261a3.png)
A.![]() | B.-1. | C.1. | D.以上答案都不对. |
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9 . 设
为
的三内角,则复数
的虚部是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1a4a91485e4c668effb85e57e80ed9.png)
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10 . 给定实数
、
、
.已知复数
、
、
满足:
求
的值.
![](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/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/d1363c663f843d356cc5539100393ffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da79a31a46bafb750eacb542bb59cd41.png)
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