Chapter 11.5, Problem 1P

Solve each equation. Check your solution.

$\frac{1}{2-j}+2=\frac{4}{2-j}$

To determine

To solve the equation and check the solutions.

Answer to Problem 1P

The solution is $j=\frac{1}{2}$ .

Explanation of Solution

Given information:

The given equation is:

  $\frac{1}{2-j}+2=\frac{4}{2-j}$

Calculation:

The solution can be obtained by:

  $\begin{array}{l}\frac{1}{2-j}+2=\frac{4}{2-j}\\ \frac{1+2\left(2-j\right)}{2-j}=\frac{4}{2-j}\\ \frac{1+4-2j}{2-j}=\frac{4}{2-j}\\ \frac{5-2j}{2-j}=\frac{4}{2-j}\\ 5-2j=\frac{4\left(2-j\right)}{2-j}\\ 5-2j=4\\ 2j=5-4\\ j=\frac{1}{2}\end{array}$

Hence, the solution is $j=\frac{1}{2}$ .

The solution can be checked by:

  $\begin{array}{l}\frac{1}{2-j}+2=\frac{4}{2-j}\\ \frac{1}{2-\frac{1}{2}}+2=\frac{4}{2-\frac{1}{2}}\\ \frac{2\times 1}{3}+2=\frac{2\times 4}{3}\\ \frac{2}{3}+2=\frac{8}{3}\\ \frac{8}{3}=\frac{8}{3}\end{array}$

The solution is correct.