If z 1 , z 2 and z 3 are the vertices of a triangle in the argand plane such that z 1 - z 2 = z 1 - z 3 , then arg ⁡ 2 z 1 - z 2 - z 3 z 3 - z 2 is

Question

If z 1 , z 2 and z 3 are the vertices of a triangle in the argand plane such that z 1 - z 2 = z 1 - z 3 , then arg ⁡ 2 z 1 - z 2 - z 3 z 3 - z 2 is, π 3, 0, π 2, π 6

MARKS App · Accepted Answer

z 1 - z 2 z 3 - z 2 = z 1 - z 2 z 3 - z 2 e i θ z 1 - z 2 z 2 - z 3 = z 1 - z 3 z 2 - z 3 e - i θ ⇒ z 1 - z 2 z 3 - z 2 + z 1 - z 3 z 3 - z 2 = purely imaginary number a r g 2 z 1 - z 2 - z 3 z 3 - z 2 = ± π 2

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