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

Question

shinalcantara · Answer

-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 $$r \angle \theta$$
$$2\sqrt{2}  \angle  135^o$$