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Question

If the complex numbers z1,z2andz3 are in AP, then they lie on a.

A
A circle
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B
A parabola
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C
Line
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D
Ellipse
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Solution

The correct option is C Line
Let z1,z2andz3 be affixes of points A, B and C respectively. Since, z1,z2andz3 in AP, therefore
2z2=z1+z3
z2=z1+z32
So, B is the mid-point of the line AC.
A, B and C are collinear.
z1,z2andz3 lie on a line.

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