Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.5

(vi) (3,2π3)(-3,-\dfrac{2\pi}{3})

Here r=3<0r=-3<0 and θ=2π3\theta=-\dfrac{2\pi}{3}.

Since r<0r<0, use angle:

2π3+π=π3-\frac{2\pi}{3}+\pi=\frac{\pi}{3} x=3cos(2π3)=32y=3sin(2π3)=332\begin{aligned} x&=-3\cos\left(-\frac{2\pi}{3}\right)=\frac{3}{2}\\ y&=-3\sin\left(-\frac{2\pi}{3}\right)=\frac{3\sqrt{3}}{2} \end{aligned}