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Question
Find the equation in cartesian coordinates of the locus of z if |z – 2 – 2i| = |z + 2 + 2i|
Solution
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
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