题目内容
（1）已知z1=5+10i，z2=3-4i，
=
+
，求z．
（2）已知（1+2i）
=4+3i，求z及
．
| 1 |
| z |
| 1 |
| z1 |
| 1 |
| z2 |
（2）已知（1+2i）
| . |
| z |
| z | ||
|
（1）∵
=
=
=
，
=
=
∴
+
=
，
故z=
=
=5-
i．
（2）∵
=
=
=2-i，
∴z=2+i，
=
=
．
| 1 |
| z1 |
| 1 |
| 5+10i |
| 5-10i |
| (5+10i)(5-10i) |
| 1-2i |
| 25 |
| 1 |
| z2 |
| 1 |
| 3-4i |
| 3+4i |
| 25 |
∴
| 1 |
| z1 |
| 1 |
| z2 |
| 4+2i |
| 25 |
故z=
| 25 |
| 4+2i |
| 25(4-2i) |
| 20 |
| 5 |
| 2 |
（2）∵
| . |
| z |
| 4+3i |
| 1+2i |
| 10-5i |
| 5 |
∴z=2+i，
| z | ||
|
| 2+i |
| 2-i |
| 3+4i |
| 5 |
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