### Complex Numbers

goals
The number of common roots of the 15th and  of 25th roots of unity are
The number of common roots of the 15th and  of 25th roots of unity are
If $\omega$ is the cube root of unity then $(1 - \omega + \omega^2)^6 =$
If $\omega$ is the cube root of unity then $(1 - \omega + \omega^2)^6 =$
The closest distance of the origin from a curve given as $a\bar z + \bar az + a\bar a = 0$ ($a$ is a complex number) is.