题目

设复数z1=a+bi，并且a2+b2=25,z2=3+4i,z1·z2是纯虚数，求z1. 答案：解：z1·z2=（a+bi）（3+4i）=（3a-4b）+（4a+3b）i.∵z1·z2是纯虚数,∴3a-4b=0且4a+3b≠0,                                    ①且a2+b2=25.                                                   ②由①和②,得或∴z1=4+3i或z1=-4-3i.

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