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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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#1 2007-08-11 02:59:21

bossk171
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complex numbers

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:



From that:



That said:



Also:



Which shows:



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.
 

#2 2007-08-11 06:01:42

kylekatarn
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Re: complex numbers

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 (2007-08-12 18:44:20)

 

#3 2007-08-12 18:43:06

kylekatarn
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Re: complex numbers

salkamat wrote:

Hmm... maybe you'll find the solution here
baseball reference

wtf?? -_-

 

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