Question

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

Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by $i$ (the conjugate of $-2i$ to eliminate imaginary denominator):
$$\frac{-4 - i}{-2i} \times \frac{i}{i} = \frac{(-4 - i)i}{-2i^2}$$

Step2: Expand numerator and simplify $i^2$

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

Step3: Split into standard form

Separate the real and imaginary parts:
$$\frac{1}{2} - 2i$$

Answer:

$\boldsymbol{\frac{1}{2} - 2i}$