Laney Spears

2022-01-31

How do you simplify $\frac{2+3i}{3-2i}$?

ebbonxah

Expert

Multiply by the complex conjugate of the denominator.
$\frac{2+3i}{3-2i}\left(\frac{3+2i}{3+2i}\right)=\frac{6+13i+6{i}^{2}}{9-4{i}^{2}}$
Recall that since $i=\sqrt{-1}$, it's true that ${i}^{2}=-1$.
$=\frac{6+13i+6\left(-1\right)}{9-4\left(-1\right)}=\frac{13i}{13}=i$

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