When tasked to find the rank/signature of say $16xy-z^2$ over $\mathbb{R}$, I proceed by writing it in the form $(2x+2y)^2-(2x-2y)^2-z^2$, and concluding that the rank is $3$, say.
For Hermitian forms, does this equivalent procedure involve using modulus brackets, or standard square brackets? I.e. if I can write a Hermitian form as $\psi(x, x) = a|A(x)|^2+b|B(x)|^2+c|C(x)|^2$ (where $a, b, c$ are all $+1$ or $-1$), can I conclude that the rank is $3$? As an example, consider Finding the rank and signature of a hermitian form