已知复数
.
(1)若z是纯虚数,求
;
(2)若
,求a,b的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5efa209c5f272365c9aa93b5256a2f4.png)
(1)若z是纯虚数,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f995b52297ee09e51312a137bbdc97a.png)
更新时间:2022-04-01 14:49:06
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【推荐1】设复数
(其中
),
.
(1)若
是实数,求
的值;
(2)若
是纯虚数,求
的虚部以及
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88701826f48dd1ea7a4869cf77d5813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab15cfa691e78c4caf7d23046df9eca.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34b88f343ca5a4c29057465541b9cf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe615164ed2995bdeea0f5b0ba94231.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a3db58264009c9fc935305c61d6607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29dbe2bfe98fe3ecc02bcff3e2a877f8.png)
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【推荐2】设复数
,求满足下列条件的实数
的值.
(1)
为实数;
(2)
为纯虚数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d75af2c5edf9f8bd85f54ee8ebdff8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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【推荐1】(1)实数
取什么数值时,复数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3487bef3a15d9216d153fd8e6b1d51b9.png)
分别是:
(i)实数? (ii)虚数? (iii)纯虚数?
(2)已知
,(
、
,
是虚数单位),求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3487bef3a15d9216d153fd8e6b1d51b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c5d66294ae9b224a962e701b13875a.png)
(i)实数? (ii)虚数? (iii)纯虚数?
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973a9cfacfdac2571cdb5d9bf64b211c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8440725e1df5ca0990b572dd84127914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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【推荐2】在①
,②z为纯虚数,③
且
对应的点在第一象限内,这三个条件中任选一个,补充在下面的问题中,并解决该问题.
已知复数
(i为虚数单位),
为z的共轭复数,若_________,求实数m的值或取值范围.(注:如果选择多个条件分别解答,按第一个条件给分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dace24e6e55291cf6c392b513179a86a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e639863c002aa3fc047212d3ff79f80f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
已知复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04cc1040c50f469cb0db58c450ca25c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
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【推荐1】在复平面
内,点
对应的复数
满足
,点
对应的复数是
,(i为虚数单位).
(1)求
;
(2)以
,
为邻边画平行四边形
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36157c54c8ee375e4bec50f4deada59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5725e7e54fcb39297e1e412bffdfe2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
(2)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e902eb263971b466d0fcd91c56b453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
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【推荐2】已知
,复数
.
(Ⅰ)若
对应的点在第四象限,求
的取值范围;
(Ⅱ)若
的共轭复数
与复数
相等,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bf497f39a09d5e41d07b84968a4a50.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23295c53a2357336b366b09498f388f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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