Question

How do I write -2+2i in polar form??

Answer 1

-2 + 2i is in the form x + yi
getting the value of r you'll have:
\[r = \sqrt{(-2)^2 +(2)^2}\]
\[r = \sqrt{8}\]
\[r = 2\sqrt{2}\]
for the angle you'll have:
\[\tan \theta = \frac{ y }{ x }\]
\[\tan \theta = \frac{ 2 }{ -2 }\]
note that in this case x is negative and y is positive therefore we can say that the angle is in the second quadrant
\[\theta = \tan^{-1} (-1)\]
\[\theta = -45^o\]
since we know that it's on the second quadrant then we'll have the angle as 180-45=135
therefore you'll have the polar form as \[r \angle \theta\]
\[2\sqrt{2} \angle 135^o\]