已知1/z=1/(1-3i)+1/(3+4i),求z

问题描述:

已知1/z=1/(1-3i)+1/(3+4i),求z

1/z=(1+3i)/(1-3i)(1+3i)+(3-4i)/(3+4i)(3-4i)=(1+3i)/10+(3-4i)/25=(11+7i)/50
所以z=50/(11+7i)=50(11-7i)/(11+7i)(11-7i)=55/17-35i/17