已知z=3+2i/1-i,复数w=z(2+i),求复w的模及w所对应点的坐标

Question

已知z=3+2i/1-i,复数w=z(2+i),求复w的模及w所对应点的坐标

Answer 1

z=(3+2i)/(1-i)=[(3+2i)(1+i)]/[(1-i)(1+i)]=(1+5i)/(1-i^2)=(1+5i)/2
w=(2+i)z=(2+i)(1+5i)/2=(-3+11i)/2=-3/2+11/2i
|w|=(-3/2)^2+(11/2)^2=9/4+121/4=130/4=65/2
对应坐标是(-3/2,11/2)