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#1 2011-06-10 02:47:27

MathPro101
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Complex Equation

I found this video on youtube of an MIT Physics lecture. If you jump ahead to around 45 minutes, the professor offers a math problem that I found interesting.

http://www.youtube.com/watch?v=OvDePn41fPY

It took me a long time to work through it, but if you know the trick, it can be solved in less than 10 seconds.


i^i, where i = sqrt(-1)

the clue is that i=e^i(pi/2 plusminus 2*pi*n), n=0,1,2,...


Have fun with it, let me know what you think.

 

#2 2011-06-19 00:40:07

soroban
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Re: Complex Equation





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#3 2011-06-19 03:54:56

MathPro101
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Re: Complex Equation

Very Good! One quick addition to that would be to say that θ = π/2 2πn, where n=0,1,2,.. This is the same as rotating on the unit circle and getting back to the same place each time. Therefore the true answer should be e^(-π/2 2πn), which is still a real number!

There is another way of solving this problem that uses a different technique. Can anyone figure that one out? It simplifies things greatly.

 

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