已知z为虚数,z+9/z−2为实数. (1)若z-2为纯虚数,求虚数z; (2)求|z-4|的取值范围.
已知z为虚数,z+
为实数.
(1)若z-2为纯虚数,求虚数z;
(2)求|z-4|的取值范围.
9 |
z−2 |
(1)若z-2为纯虚数,求虚数z;
(2)求|z-4|的取值范围.
数学人气:380 ℃时间:2019-12-20 14:06:41
优质解答
(1)设z=x+yi(x,y∈R,y≠0),则z-2=x-2+yi,由z-2为纯虚数得x=2,∴z=2+yi,…(2分)则 z+9z−2=2+yi+9yi=2+(y−9y)i∈R,…(4分)得y−9y=0,y=±3,…(6分) 所以z=2+3i或z=2-3i.…...
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