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Expression simplification/ Factorization polynomials/ z^3+i^3

Factor polynomial z^3+i^3

An expression to simplify:

The solution

You have entered [src] 
 3    3
z  + I
$$z^{3} + i^{3}$$ 
z^3 + i^3
General simplification [src] 
 3    
z  - I
$$z^{3} - i$$ 
z^3 - i
Factorization [src] 
        /            ___\ /            ___\
        |      I   \/ 3 | |      I   \/ 3 |
(x + I)*|x + - - + -----|*|x + - - - -----|
        \      2     2  / \      2     2  /
$$\left(x + i\right) \left(x + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{3}}{2} - \frac{i}{2}\right)\right)$$ 
((x + i)*(x - i/2 + sqrt(3)/2))*(x - i/2 - sqrt(3)/2)
Trigonometric part [src] 
 3    
z  - I
$$z^{3} - i$$ 
z^3 - i
Combinatorics [src] 
 3    
z  - I
$$z^{3} - i$$ 
z^3 - i
Powers [src] 
 3    
z  - I
$$z^{3} - i$$ 
z^3 - i
Common denominator [src] 
 3    
z  - I
$$z^{3} - i$$ 
z^3 - i
Combining rational expressions [src] 
 3    
z  - I
$$z^{3} - i$$ 
z^3 - i
Assemble expression [src] 
 3    
z  - I
$$z^{3} - i$$ 
z^3 - i
Numerical answer [src] 
z^3 - i
z^3 - i
Rational denominator [src] 
 3    
z  - I
$$z^{3} - i$$ 
z^3 - i
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