If the four complex numbers z , z ¯ , z ¯ - 2 Re z ¯ and z - 2 Re z represent the vertices of a square of side 4 units in the Argand plane, then z is equal to :

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Let z = x + i y ∴ length of side = 4 then z - z ¯ = 4 2 i y = 4 y = 2 also z - z - 2 Re z = 4 2 x = 4 ⇒ x = 2 z = x 2 + y 2 = 2 2

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