Question

simplify.
\\(\frac{1 + 3i}{i}\\)
write your answer in the form \\(a + bi\\). reduce all fractions.

Explanation:

Step1: Multiply numerator and denominator by $i$

$$\frac{(1+3i) \times i}{i \times i} = \frac{i + 3i^2}{i^2}$$

Step2: Substitute $i^2=-1$

$$\frac{i + 3(-1)}{-1} = \frac{i -3}{-1}$$

Step3: Simplify the expression

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

Answer:

$3 - i$