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Q.

If z1, z2, z3 are non-zero complex numbers representing the points A, B, C such that  2z1=1z2+1z3. Then

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a

Circle passes through A, B, C passes through origin.

b

None of these.

c

Circle passes through points A, B, C has centre at origin O

d

A, B, C are collinear.

answer is C.

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Detailed Solution

2z1=1z2+1z3⇒arg⁡z2−z1z3−z1=arg⁡−z2z3=arg⁡z2z3±π⇒arg⁡z2−z1z3−z1−arg⁡z2−0z3−0=±π

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