Chapter 4.4, Problem 43PPS

To determine

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

Answer to Problem 43PPS

The values of $x=2$ and $y=-3$ .

Explanation of Solution

Given:

The given equation is $x+1+2yi=3-6i$ .

Calculation:

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

The real parts

  $x+1=3$

Subtract $1$ from both sides.

  $\begin{array}{l}\Rightarrow x+1-1=3-1\\ \Rightarrow x=2\end{array}$

The imaginary parts.

  $2y=-6$

Divide both sides by $2$ .

  $\begin{array}{l}\Rightarrow \frac{2}{2}y=-\frac{6}{2}\\ \Rightarrow y=-3\end{array}$

Hence the values of $x=2$ and $y=-3$ .