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-i = i [Disproven]


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You are attempting to apply the relation [math]a^ma^n=a^{m+n}[/math] to a situation where this relation does not apply: complex numbers. You are also abusing the square root symbol, which strictly applies only to non-negative reals.

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Hey all,


Where am I making a mistake?








[math] (-1)(\sqrt{-1})\neq\sqrt{(-1)(-1)(-1)} [/math] because [math] \sqrt{a^2}=\left|a \right| [/math]


aspon myslim...

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The error in the original post ultimately lies with the implicit use of [math]\sqrt{(-1)^2}=-1[/math]. There is no need for imaginary numbers here. For example, using [math](-1)^4 = 1 = ((-1)^2)^2[/math],



1 &= \sqrt{1} \\

&= \sqrt{(-1)^4} \\

&= \sqrt{(-1)^2}\sqrt{(-1)^2} \\

&= \sqrt{(-1)^2}\sqrt{1} \\

&= (-1)\times 1 \\

&= -1



The square root function takes a branch cut at x=0. Proofs that -x=x involve an abuse of this branch cut. Don't do that!

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  • 2 weeks later...

You can proove a negative very easily, by saying,




Add x to both sides;




Divide by 2 on both sides


[math]x= \frac{1}{2} (zy^2+x)[/math]


Manipulating through algebra gives:


[math]\frac{1}{2} x-x= \frac{1}{2} (zy^2)[/math]


Solve the equation;


[math]\frac{1}{2} x= -\frac{1}{2} zy^2[/math]


Replace [math]\frac{1}{2}[/math] x with [math]\frac{1}{2}[/math] zy^2 then


[math]\frac{1}{2} x= -\frac{1}{2} x[/math]


Which is my own derivation.

Edited by MolecularEnergy
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\frac{1}{2} x-x= \frac{1}{2} (zy^2)



Here lies your mistake.


It should be:




x= \frac{1}{2} (zy^2) + \frac{1}{2} x





x - \frac{1}{2} x= \frac{1}{2} (zy^2)



Which works out fine.

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