Powers and roots of complex numbers

All the solutions of the equation $x^4+1+\sqrt{3}\mathrm{i}=0$ are complex numbers, whose arguments are from the interval $[0;2\pi )$. Find the sum of the arguments of all the solutions of the equation.

Consider an equation $x^n+b=0$, where $n$ is a positive integer and $b$ is a complex number. In the picture the points that correspond to the roots of the equation are depicted in black. Find the equation.

One solution of the equation $x^2-72i=0$ is $x_1=6(1+i)$. Find the missing solution.

Find the solution set of the following equation in the set of complex numbers. $$x^3+8\mathrm{i}=0$$