> 数学 >
已知z1=1-3i,z2=6-8i.若
1
z
+
1
z1
=
1
z2
,求z的值.
人气:331 ℃ 时间:2020-09-25 14:48:46
解答
∵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.
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