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
`(c_1)/(c_2) = (r_1)/(r_2)\text{cis}(\theta_1-\theta_2)`

So then for your problem, that would be


`(z_1)/(z_2) = \frac37\text{cis}\left(\frac\pi8-\frac\pi9\right)=\boxed{\frac37\text{cis}\left(\frac\pi{72}\right)}`

So that would be
`\boxed{\frac37\left(\cos\left(\frac\pi{72}\right)+i\sin\left(\frac\pi{72}\right)\right)}`

Hope this helps.