Question

Please help! writing in terms of i ​

Answer 1

Given:

The term is $\sqrt{-80}$.

To find:

The simplified form of the given term in terms of i.

Solution:

We have,

$\sqrt{-80}$

It can be written as:

$\sqrt{-80}=\sqrt{80\times (-1)}$

$\sqrt{-80}=\sqrt{80}\times \sqrt{-1}$

$\sqrt{-80}=\sqrt{16\times 5}\times i$         $[\because \sqrt{-1}=i]$

On further simplification, we get

$\sqrt{-80}=\sqrt{16}\times \sqrt{5}\times i$

$\sqrt{-80}=4\times \sqrt{5}\times i$

$\sqrt{-80}=4\sqrt{5}i$

Therefore, the required term is $4\sqrt{5}i$.