quote:

Originally posted by Floorfiller the square of a number cannot be negative so... i ^2 =/= -1

i is an imaginary number, it's definition is i^2 = -1 (thus sqrt(-1) = i)

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quote:

Originally posted by cheesy i is an imaginary number, it's definition is i^2 = -1 (thus sqrt(-1) = i)

alright fine then...math is stupid anyway

.999...(repeating 9's infinitely) = 1
haHA

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quote:

Originally posted by Zombie0729 sqrt(-1 * -1 ) = sqrt(-1) + sqrt(-1)

so 1 = 2i ?

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quote:

Originally posted by cheesy Yeah, what he said. sqrt( a * b ) ≠ sqrt(a) * sqrt(b)

your stamement is incorrect. sqrt(a*b) = sqrt(a)*sqrt(b). take fore example:

sqrt(16) = 4 = sqrt(4)*sqrt(4) since 16 = 4*4
sqrt(20) = 2*sqrt(5) = sqrt(4)*sqrt(5) since 20=5*4

there is another error in the original statment...

it has to do with set theory...essentially

when you have sqrt((-1)*(-1)) is where the problem starts, due to the fact that you have a sqrt of a negative number, which is in terms of real numbers undefined, because one is unable to evaluate the power series expansion for such values...

1, along with 0, is a very special number its a root of untiy

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Last edited by eulerfx on Dec-06-2004 at 04:37

quote:

Originally posted by kypez 1 = sqrt(1) = sqrt( -1 * -1 ) = sqrt(-1) * sqrt(-1) = i * i = i ^2 = -1 therefore 1 = -1 anyone know whats wrong

The Fundamental Theorem of Algebra states that an nth degree polynomial has precisely n complex roots. In particular, this means that there are n nth roots of unity. For n = 2, the roots are +/-1. That is to say, both 1 and -1 are square roots of 1.

On the other hand, the function f(x) = √2 is known as the "principal square root," and is defined as a mapping from the set of nonnegative real numbers to itself--in other words, you can only feed it nonnegative reals, and only get back nonnegative reals.

In the middle of your series of equations, you abandon this convention by taking the principal square root of -1, which is not defined. To give a shorter example, we know that

1² = -1² = 1

However, the following series of equations is false, like yours:

√1 = 1 = -1

i didnt know how to make the not equals character.

?‚

copy-paste

[edit:] whoops.

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quote:

Originally posted by Zombie0729 sqrt(-1 * -1 ) = sqrt(-1) + sqrt(-1)

guess this is why u ain't a math major

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quote:

Originally posted by vhx1 guess this is why u ain't a math major

lol, you said it. my mom would be so mad, w/ her being a calc. teacher & all