correct answer is

(2, - 3pi/4)

z= (-√2) - (i√2)

r = √(2 + 2) = 2

θ = arctan(y/x) - pi = pi/4 -pi = (-3/4) pi

as you can see at the link below, it's not that easy

anyway you should agree that writing r = -2 is a pretty bad mistake :)

It can be either:

(-2 , pi/4) or (2 , 5pi/4)

Can you tell why?

2 Angle 45 deg

z= (-√2) - (i√2)

|z|=r=√ [(-√2)^2 + (-√2)^2] = 2

arg z=Ө

ὰ=tan^-1[(Im z)/(Re z)] =tan^-1|-√2/-√2| = tan^-1(1) = π/4

as Im z <0 & Re z <0

Ө = -[π-(ὰ)] = -[π-(-π/4) = -3π/4

answer is (2,-3π/4)