Let z = x + iy
|z – 2 – 2i| = |z + 2 + 2i|
|x + iy – 2 – 2i | = |x + iy + 2 + 2i |
|(x – 2) + i(y – 2)| = |(x + 2) + i(y + 2)|
\(\sqrt{(x-2)^2+(y-2)^2}=\sqrt{(x+2)^2 + (y+2)^2}\)
(x – 2)2 + (y – 2)2 = (x + 2)2 + (y + 2)2
x2 – 4x + 4 + y2 – 4y + 4
= x2 + 4x + 4 + y2 + 4y + 4
- 4x – 4y = 4x + 4y
8x + 8y = 0
x + y = 0
y = -x