### 3.5.5 Complex numbers

When factoring polynomials, Xcas won’t introduce complex numbers if they aren’t already being used. For example,

factor(x^2 + 2)

will simply return

x^2 + 2

but if an expression already involves complex numbers then Xcas will use them;

factor(i*x^2 + 2*i)

will return

(x - i*sqrt(2))*(i*x - sqrt(2))

Xcas also has ways of finding complex roots even when complex numbers are not present; for example, the command cfactor will factor over the complex numbers

cfactor(x^2 + 2)

will return

(x - i*sqrt(2))*(x + i*sqrt(2))

If you want Xcas to use complex numbers by default, you can turn on complex mode. In complex mode,

factor(x^2 + 2)

will return

(x - i*sqrt(2))*(x + i*sqrt(2))

You can turn on complex mode from the CAS configuration screen. This mode is determined by the value of complex_mode; if this is 1 then complex mode is on, if this variable is 0 then complex mode is off. This option will be stored in the configuration file (see subsection 3.5.10), and so can also be set there.