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Question

If A(z1), B(z2) and C(z3) are three points in the argand plane where

| z1 + z2 | = | |z1| - |z2| | and | (1 - i)z1 + iz3 | = | z1 | + | z3 - z1 | ,

where i = √( -1) then

(a) A, B and C lie on a fixed circle with centre (z2 + z3)/2

(b) A, B and C are collinear points

(c) ABC form an equilateral triangle

(d) ABC form an obtuse angle triangle

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