Complex numbers: cfactor complex_mode

### 3.5.5 Complex numbers: cfactor complex_mode

When factoring polynomials (see Section 6.12.10), by default Xcas won’t introduce complex numbers if they aren’t already being used. For example,

factor(x^2 + 2)

simply returns

x2+2

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

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

will return

⎛ ⎜ ⎝ | x−i | √ |
2
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | i x− | √ |
2
| ⎞ ⎟ ⎠

Xcas can also find complex roots when complex numbers are not present; for example, the command cfactor (see Section 6.12.10) will factor over the complex numbers.
cFactor is a synonym for cfactor.

cfactor(x^2 + 2)

returns

⎛ ⎜ ⎝ | x+i | √ |
2
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | x−i | √ |
2
| ⎞ ⎟ ⎠

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

factor(x^2 + 2)

returns

⎛ ⎜ ⎝ | x+i | √ |
2
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | x−i | √ |
2
| ⎞ ⎟ ⎠

You can turn on complex mode from the CAS configuration screen (see Section 3.5.7). This mode is determined by the value of the variable complex_mode; if this is 1 then complex mode is on, if this is 0 then complex mode is off. This option will be stored in the configuration file (see Section 3.5.10), and so can also be set there.