Question

divide and express the result in standard\\(\frac{6}{3 - i}\\)

Explanation:

Step1: Multiply by conjugate of denominator

Multiply numerator and denominator by $3+i$:
$$\frac{6}{3-i} \times \frac{3+i}{3+i} = \frac{6(3+i)}{(3-i)(3+i)}$$

Step2: Expand numerator and denominator

Calculate products using distributive property:
$$\frac{18+6i}{3^2 - i^2}$$

Step3: Simplify denominator with $i^2=-1$

Substitute $i^2=-1$ and compute:
$$\frac{18+6i}{9 - (-1)} = \frac{18+6i}{10}$$

Step4: Split into standard form

Separate real and imaginary parts:
$$\frac{18}{10} + \frac{6}{10}i = \frac{9}{5} + \frac{3}{5}i$$

Answer:

$\frac{9}{5} + \frac{3}{5}i$