1 . 已知复数
满足
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46000766e2338ebce9d53c66a9e3fd9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
2 . 设
,其中
为虚数单位,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c251bf82efb628a5dcc5f3a45bba703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579743813856e2a9183f5ec6eaaefbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4753f4a4456d0df13843b71015bfa14.png)
A.![]() | B.![]() | C.1 | D.6 |
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3 . 复数
满足
(
为虚数单位),则
的共轭复数的虚部是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/573121d4915b463789a431a5bea8cec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579743813856e2a9183f5ec6eaaefbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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解题方法
4 . 已知
是复数,求
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76d384975191353e90819935ea87af5.png)
(2)若
均为实数,且复数
在复平面内对应的点位于第三象限,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76d384975191353e90819935ea87af5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd79e93f75cf5dffc6c2cdef2a33a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33071f35da5a319581f89355f68149bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-06-03更新
|
409次组卷
|
3卷引用:山东省实验中学2023-2024学年高一下学期4月期中考试数学试题
山东省实验中学2023-2024学年高一下学期4月期中考试数学试题山东省德州市夏津育中万隆中英文高级中学2023-2024学年高一下学期5月月考数学试题(已下线)必修第二册综合检测卷-重难点突破及混淆易错规避(人教A版2019必修第二册)
解题方法
5 . 欧拉公式
(其中
为虚数单位)被誉为最美数学公式.依据欧拉公式,下列选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfa007ea5744567c67bebd638bd5cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
A.复数![]() | B.![]() |
C.复数![]() ![]() | D.![]() ![]() |
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6 . 复数
满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8ce2a58c37ec50dc5130e14914243a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
A.1 | B.![]() | C.![]() | D.![]() |
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7 . 在复平面内复数
,
所对应的点为
,
,
为坐标原点,
是虚数单位.
(1)
,
,计算
与
;
(2)设
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368f9e12546277731776041c73dbe58c.png)
,求证:
,并指出向量
,
满足什么条件时该不等式取等号.
![](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/4bb8477bcc87b1401970171bf57b9ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c1fd680a5d355178273c6d6025eb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c552c2a57bd5d204c2d700ef1112554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1435039f4745c7e6fbc266636e414705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da4e6752d8c8a0705194f2b2f16ab5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f75805768bce2c1699aa5f9e33adbf4.png)
(2)设
![](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/32d3995815fb78d6abdacc08145a89b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49f7ebf36aba9ca166881222ca6aa71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30deb1f343048675b9b231620369668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1640d3fff861f45c5eb4019943b000f.png)
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解题方法
8 . 在复平面内,复数
(
是虚数单位)对应的点位于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188dced53a07aab32b91a0dc699ae27e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
A.第一象限 | B.第二象限 | C.第三象限 | D.第四象限 |
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9 . 若复数
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed98359cf005d2b49ec68f55d1f87c6e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 已知复数z在复平面内对应的点为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ded59b34148e23013fc60bb96c53ef42.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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