Concours ENSPY Practice Questions - Concours ENSPY - École Nationale Supérieure Polytechnique De Yaoundé (Cameroon) Exam

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Let $z_1 = 1 + i\sqrt{3}$ and $z_2 = 1 - i$. What is the trigonometric/polar form of the quotient $Z = \frac{z_1}{z_2}$?

Z = \sqrt{2} \left(\cos\left(\frac{7\pi}{12}\right) + i \sin\left(\frac{7\pi}{12}\right)\right) Z = \sqrt{2} \left(\cos\left(\frac{\pi}{12}\right) + i \sin\left(\frac{\pi}{12}\right)\right) Z = 2 \left(\cos\left(\frac{7\pi}{12}\right) + i \sin\left(\frac{7\pi}{12}\right)\right) Z = 1 \left(\cos\left(\frac{5\pi}{12}\right) + i \sin\left(\frac{5\pi}{12}\right)\right)

Correct Answer:

Z = \sqrt{2} \left(\cos\left(\frac{7\pi}{12}\right) + i \sin\left(\frac{7\pi}{12}\right)\right)

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