## Precalculus: Mathematics for Calculus, 7th Edition

$\sqrt \frac{-81}{16}=\frac{9}{4}i$
$i=\sqrt -1$ hence we can write $\sqrt \frac{-81}{16}$ as $\sqrt -1\times\sqrt \frac{81}{16}=\sqrt -1\times\frac{9}{4}=i\times\frac{9}{4}=\frac{9}{4}i$. Hence the answer written in the form $a+bi$ where $a$ is the real part and $b$ is the imaginary part is $\frac{9}{4}i$ as $a=0$ and $b=\frac{9}{4}$