Write an equation in vertex form for a parabola with a vertex at (-2,5) that opens down

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kristen17diaz

31.05.2023

Mathematics

Rewrite the given number as

$\dfrac{a+ib}{c+id}=\dfrac{(a+ib)(c-id)}{(c+id)(c-id)}=\dfrac{ac+bd+i(bc-ad)}{c^2+d^2}$

If it's purely real, then the complex part should be 0, so that

$\dfrac{bc-ad}{c^2+d^2}=0\implies bc-ad=0\implies\boxed{ad-bc}$

as required.

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