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Question
Find the equation in cartesian coordinates of the locus of z if |z – 3| = 2
Solution
Let z = x + iy, then
|z – 3| = 2 gives
|x + iy – 3| = 2
∴ |(x – 3) + iy| = 2
∴ `sqrt((x - 3)^2 + y^2)` = 2
∴ (x – 3)2 + y2 = 4
This is the equation of the required locus.
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