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

FalsenTo prove that the statement is false we give a counter example.nLet z_1=(1,1), z_2=(2,2), z_3=(3,3)nTherefore z_1, z_2, z_3 are in A.P.nTherefore z_1, z_2, z_3 do not lie on a circle, and are collinear.n => z_1+z_3=2 z_2

If three complex numbers are in A.P., then they lie on ... | Sequence & Series (Mathematics)

False\nTo prove that the statement is false we give a counter example.\nLet

z_1=(1,1), z_2=(2,2), z_3=(3,3)

\therefore z_1, z_2, z_3

are in A.P.\n

\therefore z_1, z_2, z_3

do not lie on a circle, and are collinear.\n

\Rightarrow z_1+z_3=2 z_2

Explanation

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