Question

Perform the indicated operation and express your answer in the form

Answer 1

Ok, so

Here we have the following expression:

`\sqrt[]{(5+12i)(12i-5)}`

We could multiply the brackets:

`\sqrt[]{60i-25+144i^2-60i}`

And then simplify:

`\sqrt[]{144i^2-25}`

Remember that

`\begin{gathered} i=\sqrt[]{-1} \\ i^2=-1 \end{gathered}`

So if we replace:

`\begin{gathered} \sqrt[]{144(-1)-25} \\ \sqrt[]{-144-25} \\ \sqrt[]{-169} \end{gathered}`

We could rewrite the last expression:

`\sqrt[]{-169}=\sqrt[]{-1}\cdot\sqrt[]{169}`

And that is:

`\sqrt[]{-1}\cdot\sqrt[]{169}=13i`

So the answer is 13i.

Written with the form a + bi:

This is 0 + 13i , which is 13i.