Question

$\frac{-9-\sqrt{-34}}{12}$

Explanation:

Step1: Rewrite the negative square root

Recall that $\sqrt{-a} = i\sqrt{a}$ for $a>0$. So $\sqrt{-34} = i\sqrt{34}$.
Expression: $\frac{-9 - i\sqrt{34}}{12}$

Step2: Split the fraction

Separate the real and imaginary parts of the complex number.
Expression: $-\frac{9}{12} - \frac{\sqrt{34}}{12}i$

Step3: Simplify the real fraction

Reduce $\frac{9}{12}$ to lowest terms.
Expression: $-\frac{3}{4} - \frac{\sqrt{34}}{12}i$

Answer:

$-\frac{3}{4} - \frac{\sqrt{34}}{12}i$