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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,582

You may be familiar with this property of square roots:

For example:

But with imaginary numbers:

Why is this ? ?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,623

MathsIsFun,

The square of (-1) is 1. The square root of 1 is ±1. Since the square root of (-1) is represented by i, and it is known that i²=-1, it may be intially baffling that -1=1, but a square root always has two values, positive and negative. In this case, since -1 is also one of the roots, the equation is perfectly right!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,582

Awww... I was hoping to cause confusion.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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