I will give 55 points please help!!! It's super important Convert the rectangular form of the complex number 2-2i into polar form. Show all work and label the modulus and argument.

polar form = [tex]r(cos \theta + i sin \theta)[/tex]
r = modulus
theta = argument

[tex]r = \sqrt{a^2 + b^2} = \sqrt{2^2 + (-2)^2} = \sqrt{8} = 2 \sqrt{2}\\ \\ tan \theta = \frac{b}{a} = \frac{-2}{2} = -1 \\ \\ \theta = \frac{7 \pi}{4} [/tex]

Note: the point '2-2i' in the complex plane is in the 4th quadrant, therefore angle must be between 3pi/2 and 2pi.

Answer:
[tex]2-2i = 2 \sqrt{2} (cos \frac{7 \pi}{4} + i sin \frac{7 \pi}{4})[/tex]