November 11th, 2009, 09:14 PM  #1 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Complex exponent
How do you evaluate (without using a calculator)? I know it is equal to 1 but I have no idea as to how to arrive at that result.

November 12th, 2009, 05:30 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Complex exponent
exp(z) = 1 + z/1 + z^2/2 + z^3/6 + z^4/24 + ... + z^k/k! + .... You can use the first halfdozen or so terms to convince yourself that it's close, or split it into parts and use limits to show the equality. Alternatively, break it into magnitude and angle components: r * exp(i * theta). The angle tells you what direction on the complex plane (0 is to the right, along the positive real axis; move counterclockwise; 2 pi is a full rotation) and the magnitude says how far. 
November 12th, 2009, 01:51 PM  #3  
Global Moderator Joined: May 2007 Posts: 6,821 Thanks: 722  Re: Complex exponent Quote:
 
November 17th, 2009, 07:39 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Complex exponent
Thanks, guys. It always amazes me how far those mathematicians got with the technology they had. Says a lot for studying, I guess. I don't know where I'd be without my calculator/computer/internet and so on. 

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