I come cross a problem when I read a book of complex analysis:
If three complex number $a,b,c$ satisfy the relation of
Prove that: these numbers must be three vertices of an equilateral triangle on the complex plane.
if $a,b,c$ are real numbers, we have $a=b=c$. but I’m not sure how to prove it with complex number. The hint I got is:
Calculate $((b-a)w+(b-c))*((b-a)w^2+(b-c))$, where $w$ is nonreal cube root of unity.