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If z1, z2, z3 are the vertices of an equilateral triangle having its circumcentre at the origin such that z1 = 1 + i, find z2 and z3.

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If z1, z2, z3 are the vertices of an equilateral triangle having its circumcentre at the origin such that z1 = 1 + i, find z2 and z3.

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Clearly, \(\vec {OB}\) and \(\vec {OC}\) are obtained by rotating \(\vec {OA}\) through 2π/3 and 4π/3 respectively.

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