Question

divide and express the result in standard form.
\\(\frac{3}{8 - i}\\)
\\(\frac{3}{8 - 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 $8+i$ (the conjugate of $8-i$):
$$\frac{3}{8-i} \times \frac{8+i}{8+i} = \frac{3(8+i)}{(8-i)(8+i)}$$

Step2: Expand numerator and denominator

Calculate the products:
Numerator: $3(8+i) = 24 + 3i$
Denominator: $(8-i)(8+i) = 8^2 - i^2 = 64 - (-1) = 65$
So we get $\frac{24 + 3i}{65}$

Step3: Split into standard form

Separate the real and imaginary parts:
$$\frac{24}{65} + \frac{3}{65}i$$

Answer:

$\frac{24}{65} + \frac{3}{65}i$