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

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

Plot the following points:

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(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}

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