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Question

If A(z1),B(z2) and C(z2) are the three points in argand plane where |z1+z2|=|z1||z2| and |(1i)z1+iz3|=|z1|+|z3z1|, then-

A
A,B and C lie on a fixed circle with centre (z2+z32)
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B
A,B,C form right angle triangle
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C
A,B,C form an equilateral triangle
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D
A,B,C form an obtuse angle triangle
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Solution

The correct options are
A A,B and C lie on a fixed circle with centre (z2+z32)
B A,B,C form right angle triangle
arg(z1z2)=±π & |z1+i(z3z1)|=|z1|+|z3z1|arg(z1z3z1)=π2
So, centre of circle =(z2+z32)
and ABC is a right angled triangle

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