# How do you simplify \frac{-3i}{5+4i}?

How do you simplify $\frac{-3i}{5+4i}$?
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Eliza Norris
Given: $\frac{-3i}{5+4i}$
Multiply by 1 in the form of $\frac{5-4i}{5-4i}$ giving:
$\frac{\left(-3i\right)\left(5-4i\right)}{\left(5+4i\right)\left(5-4i\right)}$
$\frac{-15i+12{i}^{2}}{\left(25-20i+20i-16{i}^{2}\right)}$
But ${i}^{2}=-1$ giving:
$\frac{-12-15i}{25+16}$
Therefore, $\frac{-12-15i}{41}$