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

(viii) $(-\dfrac{5}{2},\dfrac{5\pi}{12})$

Plot the following points:

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(viii) (−52,5π12)(-\dfrac{5}{2},\dfrac{5\pi}{12})

Here r=−52<0r=-\dfrac{5}{2}<0 and θ=5π12\theta=\dfrac{5\pi}{12}.

Since r<0r<0, use angle:

5π12+π=17π12\frac{5\pi}{12}+\pi=\frac{17\pi}{12}

Use:

cos⁡5π12=6−24,sin⁡5π12=6+24\cos\frac{5\pi}{12}=\frac{\sqrt{6}-\sqrt{2}}{4},\quad \sin\frac{5\pi}{12}=\frac{\sqrt{6}+\sqrt{2}}{4} x=−52cos⁡5π12=−5(6−2)8y=−52sin⁡5π12=−5(6+2)8\begin{aligned} x&=-\frac{5}{2}\cos\frac{5\pi}{12}=-\frac{5(\sqrt{6}-\sqrt{2})}{8}\\ y&=-\frac{5}{2}\sin\frac{5\pi}{12}=-\frac{5(\sqrt{6}+\sqrt{2})}{8} \end{aligned}

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