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

• February 22nd 2013, 05:00 PM
Melcarthus
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.
• February 22nd 2013, 05:03 PM
chiro
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
• February 22nd 2013, 05:12 PM
Educated
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.
• February 23rd 2013, 09:14 AM
Melcarthus
Re: How to find square root of imaginary number? Test Monday.
I got it after morning practice. :)(Happy)
• February 23rd 2013, 09:36 AM
Plato
Re: How to find square root of imaginary number? Test Monday.
Quote:

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.