Log(-1)=?

[Time And Space]

<Date 2150-13-0>

Ok you know that SquareRoot(-1)=iota

Can you please know that log(-1)=jeota

 

 

[imatfaal]

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.

[x(x-y)]

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 January 16, 2013 by x(x-y)