Chapter 4.4, Problem 22MCQ

To determine

To write: The simplification for the given expression.

Answer to Problem 22MCQ

The simplification is $\frac{1-17i}{29}$ .

Explanation of Solution

Given:

The given expression is $\frac{3-i}{2+5i}$ .

Calculation:

The expression is simplified as,

  $\begin{array}{c}\frac{3-i}{2+5i}=\frac{3-i}{2+5i}\times \frac{\left(2-5i\right)}{\left(2-5i\right)}\\ =\frac{6-15i-2i+5i^2}{4-25i^2}\\ =\frac{6-17i-5}{4+25}\\ =\frac{1-17i}{29}\end{array}$

Therefore, the simplification is $\frac{1-17i}{29}$ .