（1）已知z1=5+10i，z2=3-4i，1z=1z1+1z2，求z．（2）已知（1+2i）.z=4+3i，求z及z.z．

Question

（1）已知z ₁ =5+10i，z ₂ =3-4i， (1)/(z) = (1)/(z1) + (1)/(z2) ，求z．
（2）已知（1+2i）

.

z

=4+3i，求z及 (z)/(.z) ．

Answer 1

（1）∵ (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- (5)/(2) i．
（2）∵

.

z

= (4+3i)/(1+2i) = (10-5i)/(5) =2-i，
∴z=2+i， (z)/(.z) = (2+i)/(2-i) = (3+4i)/(5) ．