Prove three distinct complex numbers $z_1,z_2,z_3$ lie on a straight line iff $\bar{z_1}z_2+\bar{z_2}z_3+\bar{z_3}z_1=r$ which $r$ is a real number.
Why $\bar{z_1}z_2+\bar{z_2}z_3+\bar{z_3}z_1 \in \mathbb R \iff z_1, z_2, z_3 \text{ are along the same line}$