Question:
If three complex numbers z1, z2 and z3 are in A.P., then points representing them lie on ____________.
Solution:
Since z1, z2 and z3 are in A.P
Hence $2 z_{2}=z_{1}+z_{3}$
i. e $z_{2}=\frac{z_{1}+z_{3}}{z_{2}}$
i.e z2 is the mid-point of line joining z1 and z3
⇒ z1, z2 and z3 lie on a straight.
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