已知z1=1-3i，z2=6-8i．若1/z+1/z1=1/z2，求z的值．

题目

已知z₁=1-3i，z₂=6-8i．若

1

z

答案

∵z₁=1-3i，z₂=6-8i，

1

z

+

1

z1

=

1

z2

，
∴z=

z1•z2

z1−z2

=

(1−3i)(6−8i)

1−3i−(6−8i)

=

−18−26i

−5+5i

=

(−18−26i)(−5−5i)

(−5+5i)(−5−5i)

=

−40+220i

25+25

=-

4

5

+

22

5

i．