Question

perform the indicated operations.
\\(\dfrac{-4 - \sqrt{-20}}{32}\\)
\\(\dfrac{-4 - \sqrt{-20}}{32} = \square\\)
(simplify your answer. type your answer in the form \\(a + bi\\). type an exact answer, using radicals as needed. integers or fractions for any numbers in the expression.)

Explanation:

Step1: Simplify the imaginary radical

Recall that $\sqrt{-n} = i\sqrt{n}$ for positive real $n$.
$\sqrt{-20} = i\sqrt{20} = i\sqrt{4\times5} = 2i\sqrt{5}$

Step2: Substitute back into the expression

Replace $\sqrt{-20}$ with its simplified form.
$\frac{-4 - 2i\sqrt{5}}{32}$

Step3: Split the fraction

Separate the real and imaginary terms.
$\frac{-4}{32} - \frac{2i\sqrt{5}}{32}$

Step4: Simplify each fraction

Reduce the fractions to lowest terms.
$\frac{-1}{8} - \frac{i\sqrt{5}}{16}$

Answer:

$\frac{-1}{8} - \frac{\sqrt{5}}{16}i$