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

(i)

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

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(i)

z=4(cos⁡5π3+isin⁡5π3)z=4\left(\cos\frac{5\pi}{3}+i\sin\frac{5\pi}{3}\right) cos⁡5π3=12,sin⁡5π3=−32\cos\frac{5\pi}{3}=\frac{1}{2},\quad \sin\frac{5\pi}{3}=-\frac{\sqrt{3}}{2} z=4(12−32i)=2−23 i\boxed{z=4\left(\frac{1}{2}-\frac{\sqrt{3}}{2}i\right)=2-2\sqrt{3}\,i}

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