I tried this problem but was unable to figure out how to do it, could I please get a hint.
Three points, of which $1+i \sqrt{3}$ is one point, lie on the circumference of a circle of radius 2 units and centre at the origin. If these three points form the three vertices of an equilateral triangle, find the other two points.
Thank you very much!!
The angle to that point is $$ \theta_{1} = tan^{-1}\left(\frac{\sqrt{3}}{1}\right)=\frac{\pi}{3} $$ The other two points must be separated by angles of $\frac{2\pi}{3}$. Knowing that, you can do some simple trig or polar coordinates with a radius of $2$ and angles of $ \frac{\pi}{3} \pm \frac{2\pi}{3} $