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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.
#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.