Graph each system of polar equations. Solve the system using algebra and trigonometry. Assume $0 \leq \theta<2 \pi$.

$$\begin{array}{l} r=3 \\ r=2+\cos \theta \end{array}$$

Graph each polar equation. $6=r \cos \left(\theta-45^{\circ}\right)$

Use polar form to find each product or quotient. Express the result in rectangular form. $(2-2 i) \cdot(-3+3 i)$

Simplify. $(2+\sqrt{-3})(-1+\sqrt{-12})$

Graph each number in the complex plane and find its absolute value. $4+\sqrt{2} i$

Find the rectangular coordinates of each point with the given polar coordinates. $\left(6,45^{\circ}\right)$

Find the rectangular coordinates of each point with the given polar coordinates. $\left(4,210^{\circ}\right)$

Find each principal root. Express the result in the form a+bi with a and b rounded to the nearest hundredth. $(-1-i)^{\frac{1}{4}}$

Write an equation for a rose with 3 petals.

Simplify. $(1+\sqrt{7 i})(-2-\sqrt{5 i})$

Write each equation in rectangular form. $r=5 \sec \left(\theta-60^{\circ}\right)$

If $z_{1}=4\left(\cos \frac{5 \pi}{3}+i \sin \frac{5 \pi}{3}\right)$ and $z_{2}=\frac{1}{2}\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)$, find $\frac{z_{1}}{z_{2}}$ and express the result in rectangular form.

Graph each point. $M\left(2,-90^{\circ}\right)$

Find the rectangular coordinates of each point with the given polar coordinates. $\left(-2,270^{\circ}\right)$