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Question
State true or false for the following:
If three complex numbers z1, z2 and z3 are in A.P., then they lie on a circle in the complex plane.
Options
True
False
Solution
This statement is False.
Explanation:
Because if `barz_1`, z2 and z3 are in A.P.
Then z2 = `(z_1 + z_3)/2`
⇒ z2 is the midpoint of z1 and z3, which implies that the points z1, z2, z3 are collinear.
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