Chapter 8.1, Problem 7GP

To determine

The solution of the equation $-3.4=0.4j$ ,

Answer to Problem 7GP

  $j=-8.5$

Explanation of Solution

Given:

The equation, $-3.4=0.4j$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $-3.4=0.4j$ for the variable, isolate the variable term j on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate j on right side, first divide both sides by $0.4$ and then simplify further as shown below,

  $\begin{array}{c}-3.4=0.4j\\ \frac{-3.4}{0.4}=\frac{0.4j}{0.4}\\ -8.5=j\\ \Rightarrow j=-8.5\end{array}$

Thus, the solution of the given equation is $j=-8.5$ .