Chapter I, Problem 1E

To determine

To evaluate: The expression $\left(5-6i\right)+\left(3+2i\right)$ in the form of $a+bi$.

Answer to Problem 1E

The value of the expression $\left(5-6i\right)+\left(3+2i\right)$ is $8-4i$.

Explanation of Solution

The sum of two complex numbers defined as, $\left(a+bi\right)+\left(c+di\right)=\left(a+c\right)+i\left(b+d\right)$.

Thus, the expression $\left(5-6i\right)+\left(3+2i\right)$ simplified as follows.

$\begin{array}{c}\left(5-6i\right)+\left(3+2i\right)=\left(5+3\right)+i\left(-6+2\right)\\ =8-4i\end{array}$

Therefore, the value of the expression $\left(5-6i\right)+\left(3+2i\right)$ is $8-4i$.