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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.
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!