Question

watch the video and then solve the problem given below.
click here to watch the video.
perform the indicated operations.
\\(\dfrac{-7 - \sqrt{-18}}{42}\\)
\\(\dfrac{-7 - \sqrt{-18}}{42} = \square\\)
(simplify your answer. type your answer in the form \\(a + bi\\). type an exact answer, using radicals as needed. use intege

Explanation:

Step1: Simplify the imaginary radical

Recall that $\sqrt{-1}=i$. Rewrite $\sqrt{-18}$ as $\sqrt{18 \times (-1)} = \sqrt{9 \times 2} \times i = 3\sqrt{2}i$.

Step2: Substitute back into the expression

Replace $\sqrt{-18}$ with $3\sqrt{2}i$ in the original fraction:
$\frac{-7 - 3\sqrt{2}i}{42}$

Step3: Split the fraction into two terms

Separate the real and imaginary parts:
$\frac{-7}{42} - \frac{3\sqrt{2}i}{42}$

Step4: Simplify each term

Reduce the fractions to lowest terms:
$\frac{-1}{6} - \frac{\sqrt{2}}{14}i$

Answer:

$\frac{-1}{6} - \frac{\sqrt{2}}{14}i$