Chapter A.7, Problem 51AYU

To determine

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

Answer to Problem 51AYU

The given expression in the standard form $a+ib$ is $5i$ .

Explanation of Solution

Given information:

The expression is $\sqrt{\left(3+4i\right)\left(4i-3\right)}$ .

Calculation:

Consider the expression.

  $\begin{array}{c}\sqrt{\left(3+4i\right)\left(4i-3\right)}=\sqrt{-\left(3+4i\right)\left(3-4i\right)}\\ =\sqrt{-\left({\left(3\right)}^2+{\left(4i\right)}^2\right)}\\ =\sqrt{-25}\\ =\sqrt{25}\sqrt{-1}\\ =5i\end{array}$