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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?

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    Please...!!! Use Latex to write mathematics in this site...2012-10-28
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    I think if $4z^2+5w^2=4w^2+5z^2$, then you have $4(z^2-w^2)=5(z^2-w^2)$, which means $z^2-w^2=0$, so either $z=w$ or $z=-w$. Am I right?2012-10-28
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    @DonAntonio I am not very good at computers so I apologize2012-10-28
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    @user46090 okay but how can i prove the equation?2012-10-28
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    but why is it not correct? That's what i have to prove2012-10-28

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