### 5.12.10 Complex factorization : 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)