Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 1

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

Plot the following points:

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(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=−52cos⁡π3=−54y=−52sin⁡π3=−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}

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