Question

Find the quotient of the complex numbers. Leave answer in polar form.

z1 = sqrt(3)(cos 7pi/4 + i sin 7pi/4)
z2 = sqrt(6)(cos 9pi/4 +i+sin 9pi/4)

A. sqrt(2)/2 (cos 3pi/2 - i sin 3pi/2)

B. sqrt(2)/2(cos 3pi/2 - i sin 3pi/2

C. sqrt(2)/2(sin 3pi/2 +i cos 3pi/2)

D. sqrt(2)/2(cos 3pi/2 +i sin 3pi/2)

Answer 1

$\dfrac{z_1}{z_2}=\dfrac{\sqrt3}{\sqrt6}\left(\cos\left(\dfrac{7\pi}4-\dfrac{9\pi}4\right)+i\sin\left(\dfrac{7\pi}4-\dfrac{9\pi}4\right)\right)$
$\dfrac{z_1}{z_2}=\sqrt2\left(\cos\left(-\dfrac{2\pi}4\right)+i\sin\left(-\dfrac{2\pi}4\right)\right)$
$\dfrac{z_1}{z_2}=\sqrt2\left(\cos\left(-\dfrac\pi2\right)+i\sin\left(-\dfrac\pi2\right)\right)$
$\dfrac{z_1}{z_2}=\sqrt2\left(\cos\dfrac{3\pi}2+i\sin\dfrac{3\pi}2\right)$