Question

Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.

Answer 1

For any complex numbers in polar form $c_1 = r_1\text{cis}(\theta_1),\ c_2 = r_2\text{cis}(\theta_2)$

(Where $\text{cis}(\theta) = \cos(\theta) + i\sin(\theta)$)

Then $\dfrac{c_1}{c_2} = \dfrac{r_1}{r_2}\text{cis}(\theta_1-\theta_2)$

So then for your problem, that would be

$\dfrac{z_1}{z_2} = \dfrac37\text{cis}\left(\dfrac\pi8-\dfrac\pi9\right)=\boxed{\dfrac37\text{cis}\left(\dfrac\pi{72}\right)}$

So that would be $\boxed{\dfrac37\left(\cos\left(\dfrac\pi{72}\right)+i\sin\left(\dfrac\pi{72}\right)\right)}$

Hope this helps.