You have the following expression:
[tex]\pm\sqrt[]{-49}[/tex]
In order to express the previous number as an expression with the imaginary unit, you consider the following:
[tex]\begin{gathered} 49=7^2 \\ \sqrt[]{-1}=i \end{gathered}[/tex]
where the square root of -1 is the imaginary unit i by definition. Thus, by replacing you obtain:
[tex]\pm\sqrt[]{-49}=\pm\sqrt[]{(-1)(49)}=\pm\sqrt[]{(-1)(7^2)}=\pm7\sqrt[]{-1}=\pm7i[/tex]
Hence, the given expression in terms of the imaginary unit is :
[tex]\pm7i[/tex]
