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

(ii) $(-3,120^\circ)$

Plot the following points:

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(ii) (−3,120∘)(-3,120^\circ)

Here r=−3<0r=-3<0 and θ=120∘\theta=120^\circ.

Since r<0r<0, the point is 33 units from the origin in the direction θ+180∘\theta+180^\circ:

120∘+180∘=300∘120^\circ+180^\circ=300^\circ

Coordinates:

x=rcos⁡θ=−3cos⁡120∘=32y=rsin⁡θ=−3sin⁡120∘=−332\begin{aligned} x&=r\cos\theta=-3\cos 120^\circ=\frac{3}{2}\\ y&=r\sin\theta=-3\sin 120^\circ=-\frac{3\sqrt{3}}{2} \end{aligned}

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