Question

simplify.
\frac{-5 - 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 $-i$:

$$ \frac{(-5 - i)}{3i} \times \frac{-i}{-i} = \frac{(-5)(-i) + (-i)(-i)}{3i(-i)} $$

Step2: Simplify numerator and denominator

Calculate products:
Numerator: $5i + i^2 = 5i -1$
Denominator: $-3i^2 = -3(-1)=3$

$$ =\frac{-1 +5i}{3} $$

Step3: Split into standard form

Rewrite into $a+bi$:

$$ =-\frac{1}{3} + \frac{5}{3}i $$

Answer:

$\boldsymbol{-\frac{1}{3} + \frac{5}{3}i}$