Question

Express the radical using the imaginary unit, i. Express your answer in simplified form. EV -49 = =

Answer 1

You have the following expression:

$\pm\sqrt[]{-49}$

In order to express the previous number as an expression with the imaginary unit, you consider the following:

$\begin{gathered} 49=7^2 \\ \sqrt[]{-1}=i \end{gathered}$

where the square root of -1 is the imaginary unit i by definition. Thus, by replacing you obtain:

$\pm\sqrt[]{-49}=\pm\sqrt[]{(-1)(49)}=\pm\sqrt[]{(-1)(7^2)}=\pm7\sqrt[]{-1}=\pm7i$

Hence, the given expression in terms of the imaginary unit is :

$\pm7i$