If z\overline{z}=|z+\overline{z}|, where z=x+iy, i=\sqrt{-1}, then the locus of z is a pair of:

Explanation

Let z=x+iy. Given z\overline{z} = x^2+y^2 and z+\overline{z} = 2x. The equation becomes x^2+y^2=|2x|. This splits into two cases: x^2+y^2=2x or x^2+y^2=-2x. Completing the square gives (x-1)^2+y^2=1 and (x+1)^2+y^2=1. Both represent circles.

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