Question

perform the indicated operations.
\\(\frac{-4 - \sqrt{-12}}{16}\\)

\\(\frac{-4 - \sqrt{-12}}{16} = \square\\)
(simplify your answer. type your answer in the form \\(a + bi\\). type an exact answer, using radicals

Explanation:

Step1: Simplify the imaginary radical

Recall that $\sqrt{-1} = i$, so $\sqrt{-12} = \sqrt{12 \times (-1)} = \sqrt{4 \times 3}i = 2\sqrt{3}i$.

Step2: Substitute back into the expression

Replace $\sqrt{-12}$ with $2\sqrt{3}i$:
$\frac{-4 - 2\sqrt{3}i}{16}$

Step3: Split the fraction

Separate the real and imaginary parts:
$\frac{-4}{16} - \frac{2\sqrt{3}i}{16}$

Step4: Simplify each term

Reduce the fractions to lowest terms:
$\frac{-1}{4} - \frac{\sqrt{3}}{8}i$

Answer:

$\boldsymbol{-\frac{1}{4} - \frac{\sqrt{3}}{8}i}$