I know that:
$$|z| = |w| = p$$
$$4z^2 + 5w^2 = azw ,\qquad a \in R$$
I need to prove that $4w^2 + 5z^2 = azw$
How I solved it is:
$$|z| = p \implies |z|^2 = p^2 \implies zz^* = p^2$$
then solved as $z$ and replaced it to the original equation.
Then I wanted to prove that:
$$4z^2 + 5w^2 = 4w^2 + 5z^2$$ and find that $0 = 0$.
But this covers more than 5 pages and it contains lots of math, so what is an easier approach?