Question

divide and express the result in standard form.
\\(\frac{8}{6 - i}\\)
\\(\frac{8}{6 - i} = \square\\) (simplify your answer. type your answer in the form \\(a + bi\\).)

Explanation:

Step1: Multiply by conjugate of denominator

Multiply numerator and denominator by $6+i$:
$\frac{8}{6-i} \times \frac{6+i}{6+i} = \frac{8(6+i)}{(6-i)(6+i)}$

Step2: Expand numerator and denominator

Calculate products using distributive property:
Numerator: $8(6+i) = 48 + 8i$
Denominator: $(6-i)(6+i) = 6^2 - i^2 = 36 - (-1) = 37$

Step3: Split into standard form

Separate real and imaginary parts:
$\frac{48 + 8i}{37} = \frac{48}{37} + \frac{8}{37}i$

Answer:

$\frac{48}{37} + \frac{8}{37}i$