Chapter 4.4, Problem 44PPS

To determine

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

Answer to Problem 44PPS

The values of $x=-5.5$ and $y=-3$ .

Explanation of Solution

Given:

The given equation is $2x+7+\left(3-y\right)i=-4+6i$ .

Calculation:

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

The real parts

  $2x+7=-4$

Subtract $7$ from both sides.

  $\begin{array}{l}\Rightarrow 2x+7-7=-4-7\\ \Rightarrow 2x=-11\end{array}$

Divide both sides by $2$ .

  $\begin{array}{l}\Rightarrow \frac{2}{2}x=-\frac{11}{2}\\ \Rightarrow x=-5.5\end{array}$

The imaginary parts.

  $3-y=6$

Subtract $3$ from both sides.

  $\begin{array}{l}\Rightarrow 3-y-3=6-3\\ \Rightarrow -y=3\\ \Rightarrow y=-3\end{array}$

Hence the values of $x=-5.5$ and $y=-3$ .