Ok, so
Here we have the following expression:
[tex]\sqrt[]{(5+12i)(12i-5)}[/tex]
We could multiply the brackets:
[tex]\sqrt[]{60i-25+144i^2-60i}[/tex]
And then simplify:
[tex]\sqrt[]{144i^2-25}[/tex]
Remember that
[tex]\begin{gathered} i=\sqrt[]{-1} \\ i^2=-1 \end{gathered}[/tex]
So if we replace:
[tex]\begin{gathered} \sqrt[]{144(-1)-25} \\ \sqrt[]{-144-25} \\ \sqrt[]{-169} \end{gathered}[/tex]
We could rewrite the last expression:
[tex]\sqrt[]{-169}=\sqrt[]{-1}\cdot\sqrt[]{169}[/tex]
And that is:
[tex]\sqrt[]{-1}\cdot\sqrt[]{169}=13i[/tex]
So the answer is 13i.
Written with the form a + bi:
This is 0 + 13i , which is 13i.
