Problem : The complex numbers $z_1, z_2,z_3$ are satisfying $\frac{z_1-z_3}{z_2-z_3}=\frac{1-i\sqrt{3}}{2}$ $z_1,z_2,z_3$ are vertices of a triangle , which type of triangle is it :
My approach :
$|\frac{z_1-z_3}{z_2-z_3}|=|\frac{1-i\sqrt{3}}{2}| = 1 $
argument $\frac{z_1-z_3}{z_2-z_3} = \cos\frac{\pi}{3}-\sin\frac{\pi}{3}$ =$\frac{\pi}{3}$
So, I am unable to work out, whether it a isosceles or equilateral triangle. Please suggest will be of great help, thanks.