复数|Z|=√21,ARG(Z-4)=π/3,求复数Z.

复数|Z|=√21,ARG(Z-4)=π/3,求复数Z.
复数|Z|=√21,ARG(Z-4)=π/3,求复数Z.

复数|Z|=√21,ARG(Z-4)=π/3,求复数Z.
z-4=r(cosπ/3+isinπ/3)
r>0
z=(4+r/2)+ir√3/2)
所以|z|²=(4+r/2)²+(r√3/2)²=21
16+4r+r²/4+3r²/4=21
(r-1)(r+5)=0
r>0
r=1
所以z=9/2+i√3/2