题目内容


已知复数z1满足(z1-2)(1+i)=1-i(i为虚数单位),复数z2的虚部为2,且z1·z2是实数,                                                                                                                                                求z2.


解:∵(z1-2)(1+i)=1-i,

z1=2-i.

z2a+2i,a∈R,z1·z2=(2-i)(a+2i)=(2a+2)+(4-a)i.

z1·z2∈R,∴a=4,

z2=4+2i.


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