Question

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

Explanation:

Step1: Rationalize denominator

Multiply numerator and denominator by $i$:
$$\frac{(2-i) \cdot i}{2i \cdot i} = \frac{2i - i^2}{2i^2}$$

Step2: Substitute $i^2=-1$

$$\frac{2i - (-1)}{2(-1)} = \frac{1 + 2i}{-2}$$

Step3: Split into standard form

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

Answer:

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