Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.5

(v) (52,π3)(-\dfrac{5}{2},\dfrac{\pi}{3})

Here r=52<0r=-\dfrac{5}{2}<0 and θ=π3\theta=\dfrac{\pi}{3}.

Since r<0r<0, use angle:

π3+π=4π3\frac{\pi}{3}+\pi=\frac{4\pi}{3} x=52cosπ3=54y=52sinπ3=534\begin{aligned} x&=-\frac{5}{2}\cos\frac{\pi}{3}=-\frac{5}{4}\\ y&=-\frac{5}{2}\sin\frac{\pi}{3}=-\frac{5\sqrt{3}}{4} \end{aligned}