Chapter 4.4, Problem 42PPS

To determine

Find the values of the variables that make the given equation true.

Answer to Problem 42PPS

The values of $x=3$ and $y=3$ .

Explanation of Solution

Given:

The given equation is $9+12i=3x+4yi$ .

Calculation:

Set the real parts equal to each other and the imaginary parts equal to each other.

The real parts

  $9=3x$

Divide both sides by $3$ .

  $\begin{array}{l}\Rightarrow \frac{9}{3}=\frac{3}{3}x\\ \Rightarrow 3=x\\ \Rightarrow x=3\end{array}$

The imaginary parts.

  $12=4y$

Divide both sides by $4$ .

  $\begin{array}{l}\Rightarrow \frac{12}{4}=\frac{4}{4}y\\ \Rightarrow 3=y\\ \Rightarrow y=3\end{array}$

Hence the values of $x=3$ and $y=3$ .