Question

$\frac{-9-\sqrt{-36}}{12}=$
(type an exact

Explanation:

Step1: Simplify the imaginary square root

Recall that $\sqrt{-1}=i$, so $\sqrt{-36}=\sqrt{36\times(-1)}=\sqrt{36}\times\sqrt{-1}=6i$.

Step2: Substitute back and split the fraction

Substitute $\sqrt{-36}=6i$ into the expression, then split the fraction into two terms:
$\frac{-9 - 6i}{12}=\frac{-9}{12}-\frac{6i}{12}$

Step3: Simplify each fraction

Reduce the fractions to lowest terms:
$\frac{-9}{12}=-\frac{3}{4}$, $\frac{6i}{12}=\frac{1}{2}i$

Answer:

$-\frac{3}{4}-\frac{1}{2}i$