Please help! Pre calc questions!

9.)

$r\ =\ \frac{4}{2\cos\theta-3\sin\theta}\\~\\ r(2\cos\theta-3\sin\theta)\ =\ 4\\~\\ 2r\cos\theta-3r\sin\theta\ =\ 4\\~\\ 2x-3y\ =\ 4\qquad\ \qquad\ \qquad\text{because}\qquad x=r\cos\theta\qquad\text{and}\qquad y=r\sin\theta\\~\\ 2x\ =\ 4+3y\\~\\ 2x-4\ =\ 3y\\~\\ \frac23x-\frac43\ =\ y\\~\\ y\ =\ \frac23x-\frac43$

This is the equation of a line with a slope of   $\frac23$   and a y-intercept of  $-\frac43$ .

Check: https://www.desmos.com/calculator/7dq2bqym7k

(You can show or hide the second equation by clicking the gray circle to the left of it. )

10.) compute the modulus and argument of each complex number.

 a.)   -5

We have the form      -5 + 0i

The modulus is   √ [ (-50^2 + 0^2 ]  =  √25  = 5

The argument is θ  so   tan θ  =   0 / -5  =  pi

b. )  -5 + 5i

Modulus  =  √[ (-5)^2 + (5)^2 ]  = √ [ 50]  = 5√2

The argument is θ  so   tan θ  =  5/-5  = - 1  =  3pi/4