Math Is Fun Forum

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Imaginary Confusion

You may be familiar with this property of square roots:

For example:

But with imaginary numbers:

Why is this ? ?

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

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,464

Re: Imaginary Confusion

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!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Imaginary Confusion

Awww... I was hoping to cause confusion.

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