Why does factor() assume that variables are real?

edit

To clarify @FrédéricC's answer :

sage: var("z1, z2", domain="complex")
(z1, z2)
sage: term=z1*z2.conjugate()-z2*z1.conjugate()
sage: term
-z2*conjugate(z1) + z1*conjugate(z2)
sage: term.factor()
-z2*conjugate(z1) + z1*conjugate(z2sage: var("a, b, c, d", domain="real")
(a, b, c, d)
sage: term.subs({z1: a+I*b, z2:c+I*d})
-(a - I*b)*(c + I*d) + (a + I*b)*(c - I*d)
sage: term.subs({z1: a+I*b, z2:c+I*d}).factor()
2*I*b*c - 2*I*a*d
sage: term.subs({z1: a+I*b, z2:c+I*d}).collect_common_factors()
-(a - I*b)*(c + I*d) + (a + I*b)*(c - I*d)

(Maxima's) factor seems to sloppily assume that a typeless symbolic variable is real. This bug should be more filed, explored and possibly reported to Maxima's developpers.

HTH,

Indeed, in (native) Maxima 5.47.0 :

(%i2) factor(z1*conjugate(z2)-z2*conjugate(z1));
(%o2)                                  0

HTH,