For any complex numbers in polar form [tex]c_1 = r_1\text{cis}(\theta_1),\ c_2 = r_2\text{cis}(\theta_2)[/tex]
(Where [tex]\text{cis}(\theta) = \cos(\theta) + i\sin(\theta)[/tex])
Then [tex]\dfrac{c_1}{c_2} = \dfrac{r_1}{r_2}\text{cis}(\theta_1-\theta_2)[/tex]
So then for your problem, that would be
[tex]\dfrac{z_1}{z_2} = \dfrac37\text{cis}\left(\dfrac\pi8-\dfrac\pi9\right)=\boxed{\dfrac37\text{cis}\left(\dfrac\pi{72}\right)}[/tex]
So that would be [tex]\boxed{\dfrac37\left(\cos\left(\dfrac\pi{72}\right)+i\sin\left(\dfrac\pi{72}\right)\right)}[/tex]
Hope this helps.
