# Thread: How to find square root of imaginary number? Test Monday.

1. ## How to find square root of imaginary number? Test Monday.

So under the square root number is a negative 8. Should be 2*sqr root of 2. How to they get there? Where does imaginary symbol go usually? Any video links,sites, diagrams will be helpful plz.

2. ## Re: How to find square root of imaginary number? Test Monday.

Hey Melcarthus.

The simplest answer is to use the polar form of a complex number and use the rules of exponentiation.

Complex number - Wikipedia, the free encyclopedia

3. ## Re: How to find square root of imaginary number? Test Monday.

This is one of the first things you should have learnt when studying imaginary numbers...

$\sqrt{-8} = \sqrt{8} \cdot \sqrt{-1} = \sqrt{8}i = 2 \sqrt{2}i$

The i is not under the square root.

The title is also quite misleading. You are trying to find the square root of a negative number, not the square root of an imaginary number. It's more complicated when you are trying to find the square root of an imaginary number.

4. ## Re: How to find square root of imaginary number? Test Monday.

I got it after morning practice.

5. ## Re: How to find square root of imaginary number? Test Monday.

Originally Posted by Melcarthus
So under the square root number is a negative 8. Should be 2*sqr root of 2. How to they get there? Where does imaginary symbol go usually? Any video links,sites, diagrams will be helpful plz.

$(\sqrt{8}i)^2=(2\sqrt2i)^2=-8$

Now that is a simple answer.