Question

simplify.
\frac{-4 - 2i}{3i}
write your answer in the form a + bi. reduce all fractions.

Explanation:

Step1: Rationalize denominator

Multiply numerator/denominator by $i$:
$$\frac{(-4 - 2i) \cdot i}{3i \cdot i}$$

Step2: Expand numerator and denominator

$$\frac{-4i -2i^2}{3i^2}$$
Substitute $i^2=-1$:
$$\frac{-4i -2(-1)}{3(-1)} = \frac{2 -4i}{-3}$$

Step3: Split and simplify fraction

$$-\frac{2}{3} + \frac{4}{3}i$$

Answer:

$\boldsymbol{-\frac{2}{3} + \frac{4}{3}i}$