# If three complex numbers

Question:

If three complex numbers z1z2 and z3 are in A.P., then points representing them lie on ____________.

Solution:

Since z1z2 and zare 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 zand z3

⇒ z1z2  and zlie on a straight.