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._刷题宝

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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.

上一题下一题 0.0难度选择题更新时间:2019-11-19 05:18:51

答案(点此获取答案解析）

(z₁－2)(1＋i)＝1－i⇒z₁＝2－i，

设z₂＝a＋2i，a∈R，

则z₁z₂＝(2－i)(a＋2i)＝(2a＋2)＋(4－a)i，

∵z₁z₂∈R，∴a＝4，∴z₂＝4＋2i.

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