/sci/ - Science & Math

"why not?"
You might be interested in some visualizations of the Log, and other functions, in the complex plane, to get some intuition. But for the thing you posted, I guess you could just derive the latter from the former via splitting z into r*exp(iv) and treating r as a complex number with argument equal to zero.

Log(1/z)
= Log(1/(r*exp(iv))
= Log(exp(-iv)/r)
= Log(exp(-iv)) + Log(1/r)
= - iv - Log(1/r)
= - (iv + Log(r))
= - (Log(exp(iv)) + Log(r))
= - Log(exp(iv)*r)
= - Log(z)

I.e. "why not", the second formula only involves one number which is properly complex, the first says something about two.

4 = 2 * 2 = -1 * -2 * √4 = -1 * √(-2)2*4 = -1 * √16 = -4

Why are we made this way?

What did people invent bifurication theory for?

will humans continue to evolve?