Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 3

(ii)

Convert each of the complex numbers $z$ in the rectangular form $x+iy$:

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(ii)

z=32(cos⁡7π6+isin⁡7π6)z=\frac{3}{2}\left(\cos\frac{7\pi}{6}+i\sin\frac{7\pi}{6}\right) cos⁡7π6=−32,sin⁡7π6=−12\cos\frac{7\pi}{6}=-\frac{\sqrt{3}}{2},\quad \sin\frac{7\pi}{6}=-\frac{1}{2} z=32(−32−12i)=−334−34i\boxed{z=\frac{3}{2}\left(-\frac{\sqrt{3}}{2}-\frac{1}{2}i\right)=-\frac{3\sqrt{3}}{4}-\frac{3}{4}i}

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