已知z1=5+10i,z2=3-4i,1/z=1/z1+1/z2,求z.RT、_数学解答

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

人气：144 ℃　时间：2020-04-16 09:43:06

解答

1/z=(z1+z2)/(z1z2)
z=(5+10i)(3-4i)/(5+10i+3-4i)
=(15+40-20i+30i)/(8+6i)
=(55-10i)(8-6i)/(8+6i)(8-6i)
=5(88-66i-16i-12)/(64+36)
=(76-82i)/20
=(38-41i)/10