复数z的模是1╱2+（√3╱2）i的两倍,辐角主值是它的辐角主值的两倍,求复数z的值

Question

复数z的模是1╱2+（√3╱2）i的两倍,辐角主值是它的辐角主值的两倍,求复数z的值

Answer 1

∵1/2+(√3/2)i的模是√((1/2)²+(√3/2)²)=1
幅角主值是arctan((√3/2)/(1/2))=π/3
∴z的模是2,幅角主值是2π/3
z的实部是2×cos(2π/3)=-1
虚部是2×sin(2π/3)=√3
∴z=-1+√3i