On Wed, 15 Feb 2012 at 06:15AM +0000, Dr. David Kirkby wrote: > What is sqrt(i), and why?
As for sqrt(i), if you represent it as exp(i*pi/2), there are two numbers z that satisfy z^2 = i, namely exp(i*pi/4) and exp(i*5*pi/4). Look up the polar form of complex numbers. As for why: well, why should non-integer powers be reserved for real numbers? If I can find a number w so that w^2 = z, who wouldn't call that the/a square root root of z? Math would make no sense if we arbitrarily decided to not do things in the complex numbers even though they are simple and easy to imagine. > Put me out of my misery. I should hope that learning the polar form of complex numbers doesn't cause anyone misery! Dan -- --- Dan Drake ----- http://mathsci.kaist.ac.kr/~drake -------
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