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Log(-1)=?


Time And Space

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no - square root of minus one is i not iota

 

and bearing in mind euler's identity there is no need to specify a new symbol for the natural log of minus one, it is equal to pi times i

 

You will get much further by adopting well-worn mathematical ideas - and adapting to your own purposes than by trying to re-invent and rename ideas that have existed for many hundreds of years. you might well be a better mathematician than me - but I would bet you are not a better mathematician than Euler.

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Indeed, as imatfaal stated, one can easily derive an "imaginary expression" for the natural logarithm of a negative number by applying Euler's identity:

 

[latex]Ne^{i\pi} = -N[/latex]

 

where [latex]N \in \mathbb{R}[/latex]

 

[latex]\Rightarrow \ln\left(Ne^{i\pi}\right) = \ln(-N)[/latex]

 

[latex]\Rightarrow \ln N + \ln e^{i\pi} = \ln (-N)[/latex]

 

[latex]\therefore \ln (-N) = i\pi + \ln N[/latex]

 

 

Edited by x(x-y)
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