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Question

If three complex numbers are in A.P., then they lie on


A

A circle in the complex plane

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B

A straight line in the complex plane

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C

A parabola in the complex plane

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D

None of these

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Solution

The correct option is B

A straight line in the complex plane


Let z1,z2,z3 be three complex numbers in A.P.

Then 2z2=z1+z3.

Thus the complex number z2 is the mid-point of the line joining the points z1 and z3 so the three points z1,z2 and z3 are in a straight line.


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