Chapter A.7, Problem 23AYU

To determine

To write:The given expression in the standard form $a+ib$ .

Answer to Problem 23AYU

The given expression in the standard form $a+ib$ is $\frac{6}{5}+\frac{8}{5}i$ .

Explanation of Solution

Given information:

The expression is $\frac{10}{3-4i}$ .

Calculation:

Consider the expression.

$\begin{array}{c}\frac{10}{3-4i}=\frac{10}{3-4i}\frac{\left(3+4i\right)}{\left(3+4i\right)}\\ =\frac{30+40i}{3\left(3+4i\right)-4i\left(3+4i\right)}\\ =\frac{30+40i}{9+12i-12i+16}\\ =\frac{30+40i}{25}\\ =\frac{6}{5}+\frac{8}{5}i\end{array}$