An elementary question about real inflection points of cubics:
Textbooks mention that non-singular cubics in $P^2(C)$ have 3 real and 6 complex inflections and show the Hesse normal form $ x^3 + y^3 + z^3 + 3m xyz=0 $, $m \in C $, $ m^3 \neq 1$, with the usual table of its 9 inflections $ (0, 1, -1), ..., (1, \exp(2 \pi i/3), 0)$ .
Does every non-singular cubic $ \ F(x,y,z) = \Sigma a_{i,j} x^i y^j z^{3-i-j} = 0 \ $ has 3 real inflections even if $a_{i,j}$ are complex valued? Or is it true only for real cubics with real $a_{i,j}$ ? Is there a reference which states this clearly?
