According to Evar Nering's "Linear Algebra and Matrix Theory", 2nd edition, (12.4 on page 172; full text here: https://archive.org/details/LinearAlgebraAndMatrixTheory/page/n4), the underlying bilinear form of a Hermitian quadratic form can be obtained by the following:
$f(a, b) = 1/4[q(a + b) - q(a - b) - iq(a + ib) + iq(a - ib)]$
where f is the bilinear form, $q$ is a Hermitian form, a and b are any two vectors, and $i=\sqrt{-1}$.
Can anyone please explain how this relationship can be derived or be shown to be true? (A similar relationship for quadratic forms is derived in 9.1 on page 161 of the text. I'm having problems applying the same reasoning to the case above.)
Thank you.