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If |z - 2/z + 2| = π/6  then the locus of z is ………….

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If |z - 2/z + 2| = π/6  then the locus of z is ………….

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⇒ 6 |x – 2 + iy| = π |x + 2 + iy|

Squaring on both sides,

⇒ 36 |x – 2 + iy|2 = π2 |x + 2 + iy|2

⇒ 36 [x2 – 4x + 4 + y2] = π2 [x2 – 4x + 4 + y2]

⇒ (36 – π2) x2 + (36 – π2) y2 – (144 + 4π2) x + 144 – 4π2 = 0

Which is a circle.

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