已知复数│z-1│=2√3,arg(z+1)=2π/3,求复数Z

因为arg(z+1)=2π/3所以设z+1=r(cos2π/3+isin2π/3)=-1/2r+√3/2ir(r>0)所以z-1=-1/2r-2+√3/2ir所以|z-1|=√((1/2r+2)^2+(√3/2r)^2)=2√3,得r=2所以z=-2+√3i