Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2007-02-08 20:05:33

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Imaginary Confusion

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

Offline

#2 2007-02-09 16:41:55

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,969

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! dizzy


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.

Offline

#3 2007-02-09 19:04:26

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: Imaginary Confusion

Awww... I was hoping to cause confusion.


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

Offline

Board footer

Powered by FluxBB