Question

simplify.
\\(\frac{1 - 2i}{4i}\\)
write your answer in the form \\(a + bi\\). reduce all fractions.

Explanation:

Step1: Multiply numerator/denominator by $i$

$$\frac{(1-2i) \cdot i}{4i \cdot i}$$

Step2: Expand numerator and denominator

$$\frac{i - 2i^2}{4i^2}$$

Step3: Substitute $i^2=-1$

$$\frac{i - 2(-1)}{4(-1)}=\frac{i +2}{-4}$$

Step4: Rewrite in $a+bi$ form

$$-\frac{2}{4} - \frac{1}{4}i = -\frac{1}{2} - \frac{1}{4}i$$

Answer:

$\boldsymbol{-\frac{1}{2} - \frac{1}{4}i}$