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Question

If z1,z2,z3 are the vertices of a triangle in argand plane such that |z1z2|=|z1z3|, then arg(2z1z2z3z3z2) is

A
±π3
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B
0
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C
±π2
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D
±π6
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Solution

The correct option is C ±π2

z1z2z3z2=|z1z2||z3z2|eiθ
z1z3z2z3=|z1z3||z2z3|eiθ
z1z2z3z2+z1z3z3z2=Purely imaginary number
So, arg(2z1z2z3z3z2)=±π2

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