<s>[INST] Sum of non-real roots of equation? What is the sum of all non-real, complex roots of this equation -
$$x^5 = 1024$$
Also, please provide explanation about how to find sum all of non real, complex roots of any $n$ degree polynomial. Is there any way to determine number of real and non-real roots of an equation?

Please not that I'm a high school freshman (grade 9). So please provide simple explanation. Thanks in advance!
 [/INST] $\bf{My\; Solution::}$ Given $$x^5 = 1024 = 2^{10} = 4^5\Rightarrow x^5-4^5 = 0$$
So $$(x^5-4^5) = (x-5)\cdot (x^4+x^3\cdot 4+x^2\cdot 4^2+x\cdot 4^3+4^4) = 0$$
Above we use the formula $\displaystyle x^n-a^n = (x-a)\cdot (x^{n-1}+x^{n-2}\cdot a+x^{n-3}\cdot a^2+.......+a^{n-1})$
So We Get $x=4(\bf{Real \; Root})$ and $$x^4+x^3\cdot 4+x^2\cdot 4^2+x\cdot 4^3+4^4=0$$
So Sum of Roots in $\bf{Second}$ Equation is $\displaystyle = -\frac{4}{1} = -4$ 
Above we use the Formula $\displaystyle \bf{Sum\; of \; Roots} = -\frac{\bf{coeff.\; of \; x^3}}{\bf{coeff.\; of \; x^4}}$
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