Factor polynomial z^3+1-i

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 3        
z  + 1 - I

$$\left(z^{3} + 1\right) - i$$

z^3 + 1 - i

Factorization [src]

/       2/3      2/3\ /     2/3      2/3    2/3   ___      2/3   ___\ /     2/3      2/3    2/3   ___      2/3   ___\
|      2      I*2   | |    2      I*2      2   *\/ 3    I*2   *\/ 3 | |    2      I*2      2   *\/ 3    I*2   *\/ 3 |
|x + - ---- - ------|*|x + ---- + ------ - ---------- + ------------|*|x + ---- + ------ + ---------- - ------------|
\       2       2   / \     4       4          4             4      / \     4       4          4             4      /

$$\left(x + \left(- \frac{2^{\frac{2}{3}}}{2} - \frac{2^{\frac{2}{3}} i}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{2}{3}} \sqrt{3}}{4} + \frac{2^{\frac{2}{3}}}{4} + \frac{2^{\frac{2}{3}} i}{4} + \frac{2^{\frac{2}{3}} \sqrt{3} i}{4}\right)\right) \left(x + \left(\frac{2^{\frac{2}{3}}}{4} + \frac{2^{\frac{2}{3}} \sqrt{3}}{4} - \frac{2^{\frac{2}{3}} \sqrt{3} i}{4} + \frac{2^{\frac{2}{3}} i}{4}\right)\right)$$

((x - 2^(2/3)/2 - i*2^(2/3)/2)*(x + 2^(2/3)/4 + i*2^(2/3)/4 - 2^(2/3)*sqrt(3)/4 + i*2^(2/3)*sqrt(3)/4))*(x + 2^(2/3)/4 + i*2^(2/3)/4 + 2^(2/3)*sqrt(3)/4 - i*2^(2/3)*sqrt(3)/4)

General simplification [src]

     3    
1 + z  - I

$$z^{3} + 1 - i$$

1 + z^3 - i

Trigonometric part [src]

     3    
1 + z  - I

$$z^{3} + 1 - i$$

1 + z^3 - i

Rational denominator [src]

     3    
1 + z  - I

$$z^{3} + 1 - i$$

1 + z^3 - i

Numerical answer [src]

1.0 + z^3 - i

1.0 + z^3 - i

Assemble expression [src]

     3    
1 + z  - I

$$z^{3} + 1 - i$$

1 + z^3 - i

Combining rational expressions [src]

     3    
1 + z  - I

$$z^{3} + 1 - i$$

1 + z^3 - i

Common denominator [src]

     3    
1 + z  - I

$$z^{3} + 1 - i$$

1 + z^3 - i

Powers [src]

     3    
1 + z  - I

$$z^{3} + 1 - i$$

1 + z^3 - i

Combinatorics [src]

     3    
1 + z  - I

$$z^{3} + 1 - i$$

1 + z^3 - i

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Factor polynomial z^3+1-i

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