Properties of TriangleHard

Question

If the points A(z), B(-z) and c(1 - z) are the vertices of an equilateral triangle ABC then Re(z) is equal to :-

Options

A.
B.
C.
D.None

Solution


AB = BC = CA
|2z| = 1 = |2z - 1|; 2|z| = 1
(2z - 1) (2 - 1) = 1
4|z|2 - 2(z + ) + 1 = 1
1 - 2(2x) = 0
x =      Re(z) =

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