Question

simplify.
\\(\frac{3 + i}{3i}\\)
write your answer in the form \\(a + bi\\). reduce all fractions.

Explanation:

Step1: Multiply by conjugate of denominator

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

Step2: Expand numerator and simplify denominator

$$\frac{-3i -i^2}{-3i^2} = \frac{-3i +1}{3}$$

Step3: Split into standard form

Rewrite as separate real and imaginary terms:
$$\frac{1}{3} - \frac{3}{3}i = \frac{1}{3} - i$$

Answer:

$\frac{1}{3} - i$