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

`(z_1)/(z_2)=(\sqrt3)/(\sqrt6)\left(\cos\left(\frac{7\pi}4-\frac{9\pi}4\right)+i\sin\left(\frac{7\pi}4-\frac{9\pi}4\right)\right)`

`(z_1)/(z_2)=\sqrt2\left(\cos\left(-\frac{2\pi}4\right)+i\sin\left(-\frac{2\pi}4\right)\right)`

`(z_1)/(z_2)=\sqrt2\left(\cos\left(-\frac\pi2\right)+i\sin\left(-\frac\pi2\right)\right)`

`(z_1)/(z_2)=\sqrt2\left(\cos\frac{3\pi}2+i\sin\frac{3\pi}2\right)`