Question

If |z|=2 and arg (z)=pi/4, find z

Answer 1

here is your answer

arg(z) = 2tan-1yx2+y2+x=π4 where z=x+iy ----------(1)and |z|=x2+y2=2 ------------------(2)solving equation (1) and (2) we can gety2+x=tan(π8)x=-2 and y=0so z=-2+0i