Chapter 4.4, Problem 19PPS

To determine

Find the simplified form of the given expression.

Answer to Problem 19PPS

The simplified form of the expression is $13i$ .

Explanation of Solution

Given:

The given expression is $\sqrt{-169}$ .

Calculation:

Pure imaginary number $\to$ it is a square root of negative real number. For any positive real number $b$ , $\sqrt{-b^2}=\sqrt{b^2}\cdot \sqrt{-1}\text{or}bi$ . The number $i$ is the principal square root of $-1$ ; that is, $i=\sqrt{-1}$ .

  $\begin{array}{l}\sqrt{-169}\\ =\sqrt{-1\cdot 169}\\ =\sqrt{-1}\cdot \sqrt{{13}^2}\\ =i\cdot 13\\ =13i\end{array}$

Hence the simplified form of the expression is $13i$ .