this is a question on my homework that I am just lost with. Some direction would be greatly appreciated.
Write $z_1$ and $z_2$ in polar form, and then find the product $z_{1}z_{2}$ and the quotients $z_1/z_2$ and $1/z_1$. (Express your answers in polar form.)
$z_1 = \sqrt{2}-\sqrt{2}i, \ z_2 = 3-3i$
I have calculated the modulus for each as $2$ and $3\sqrt{2}$ respectively. This I believe is correct as it is a simple formula. I then calculated the theta of each as $\pi/4$ for both of them, this was using $\arctan(\sqrt{2}/\sqrt{2})$ and $\arctan(3/3)$ respectively. Now when I drop them into place for $z_{1}z_{2}$ I receive:
$\begin{align*} 6 \sqrt{2}\Bigl(\cos(\pi/2)+i \sin(\pi/2)\Bigr)&= 6\sqrt{2}\Bigl(0+i1\Bigr)\\ &= 6\sqrt{2}i\\ &= z_{1}z_{2} \end{align*}$ Am I just making incorrect calculations or missing something? Apologies for my lack of MathJaX knowledge. Thanks for any help.