Q. 598 - Intermediate Algebra

Question

In the following exercises, simplify. Assume all variables are positive.

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

Step-by-Step Solution

Answer

The simplified expression is $\frac{10}{13}+i\frac{11}{13}$

Step 1. Given Information

We have

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

Step 2. Multiply and divide by conjugate

$$\begin{gathered} \frac{4+i}{3-2i}\times \frac{3+2i}{3+2i} \\ =\frac{\left(4+i\right)\left(3+2i\right)}{3^2-{\left(2i\right)}^2} \end{gathered}$$

Step 3. Simplify the rational expression

$$\begin{gathered} \frac{12+8i+3i+2i^2}{9+4}=\frac{12+11i-2}{13} \\ =\frac{10+11i}{13}=\frac{10}{13}+i\frac{11}{13} \end{gathered}$$