### 2.12.10 Complex factorisation : `cFactor`

`cFactor` takes as argument an expression.
`cFactor` factorizes this expression on the field ℚ[i] ⊂ ℂ (or over the complexified field of the coefficients of the argument) even if you are in real mode.
Examples

1. Factorize x4−1 over ℤ[i].
   Input :
   `cFactor(x```^```4-1)`
   Output :
   `-((x+-i)*((-i)*x+1)*((-i)*x+i)*(x+1))`
2. Factorize x4+1 over ℤ[i].
   Input :
   `cFactor(x```^```4+1)`
   Output :
   `(x```^```2+i)*(x```^```2+-i)`
3. For a complete factorization of x4+1, check the sqrt box in the Cas configuration or input :
   `cFactor(x```^```4+1,sqrt(2))`
   Output :
   `sqrt(2)*1/2*(sqrt(2)*x+1-i)*(sqrt(2)*x-1+i)*sqrt(2)* 1/2*(sqrt(2)*x+1+i)*(sqrt(2)*x-1-i)`