已知z1=5+10i，z2=3-4i，1z＝1z1+1z2，求z．

Question

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

Answer 1

(1)/(z)＝(1)/(z1)+(1)/(z2)＝(z1+z2)/(z1z2)
∴z＝(z1z2)/(z1+z1)
又∵z₁=5+10i，z₂=3-4i
∴z＝((5+10i)(3−4i))/(5+10i+3−4i)＝(55+10i)/(8+6i)＝((55+10i)(8−6i))/((8+6i)(8−6i))＝ 5−(5)/(2)i