Complex Numbers in Rectangular, Polar Form Practice Test

Convert $5\big(\cos 30^\circ+i\sin 30^\circ\big)$ from polar form to rectangular form $a+bi$. Use $a=r\cos\theta$ and $b=r\sin\theta$. (The argument is the angle from the positive real axis.)

An AC current is represented by the complex number $z=-3+3i$ amps in rectangular form $a+bi$. Convert it to polar form $r(\cos\theta+i\sin\theta)$, where $r=\sqrt{a^2+b^2}$ and $\theta=\arctan(b/a)$ with quadrant adjustment. Give $\theta$ in degrees as the argument measured from the positive real axis.