and so [tex]x^2+ y^2= r^2 cos^2(\theta)+ r^2 sin^2(\theta)= r^2[/itex]: . Dividing y by x, and [tex]\theta= arctan(y/x)[/itex].

Here, so r= 2. [tex]y/x= -1/\sqrt{3}[tex] so [tex]tan(\theta)= -1/\sqrt{3}[/itex] and .

Once you have Z in polar form, has and [tex]\theta= 8(-\pi/6)= -4\pi/3[/itex]. The real part of is and the imaginary part is .