If the complex numbers $z_1,z_2,z_3$ are in A. P., then they lie on a 

$z_2=\frac{z_1+z_3}{2}\Rightarrow z_2$ is mid-point of line joining 

$z_1\text{ and }{z}_3$. Hence they lie on a line. 

Alt. When we say that complex numbers are in A. P., it means that their moduli are in A. P. Consider

$e^{\pi i/3},3e^{\pi i/3},5e^{\pi i/3}$. Their three moduli 1, 3, 5 are in A.P.

 They clearly lie on the line $\theta =\pi /3$.