Answer:
(2[tex]\sqrt{2}[/tex], 135° )
Step-by-step explanation:
To convert from rectangular to polar form, that is
(x, y ) → (r, Θ ), with
r = [tex]\sqrt{x^2+y^2}[/tex]
tanΘ = [tex]\frac{y}{x}[/tex]
Given - 2 + 2i, then
r = [tex]\sqrt{(-2)^2+2^2}[/tex] = [tex]\sqrt{4+4}[/tex] = [tex]\sqrt{8}[/tex] = 2[tex]\sqrt{2}[/tex]
Since - 2 + 2i is in the second quadrant then Θ must be in the second quadrant.
tanΘ = [tex]\frac{2}{-2}[/tex] = - 1, thus
Θ = [tex]tan^{-1}[/tex] (- 1) = - 45°, hence
Θ = 180° - 45° = 135° ← in second quadrant
Thus
- 2 + 2i → (2[tex]\sqrt{2}[/tex], 135° )
