This is something that's been bothering me for some time, and I thought starting a post on in might help me out. I'm not posting it in the "Help Me" forum, because instead of a question, I was hoping for an open dialog. If some one feels this is the wrong place, then pleas move it to "Help Me."
This is as far as I've gotten:
With a similar method (that is kind of tedious to do out) I found:
I get how to find the kth root of any imaginary number, but I can't make a general rule, I have to do each out by hand.
Using Taylor series I can show :
And from there I think I get k^i, but only if k is a real number.
which leaves me with the following questions:
That last one is a calculator answer, but why?
Any other I properties would be fun to see, so if anyone else has something to offer, please, I'd like to learn as much as I can about complex numbers.
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
complex logarithm: clog(r*exp(i.t)) = ln(r)+i.t
i^i = exp(i clog(i)) = exp(i ( ln(1) + i.pi/2))) = exp(i^2. pi/2) = exp(-pi/2) = 0.2078...
Last edited by kylekatarn (2007-08-11 20:44:20)