Oct 3, 2015 · A pedantic point: is a complex number with a 0 imaginary part the same as a real number?

May 11, 2015 · There are multiple ways of writing out a given complex number, or a number in general. Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot …

Aug 30, 2010 · First, a concrete example of things that can happen with complex exponentiation if you aren't careful: $1 = e^ {2\pi i}$, so we can naively try to compute $1^i = (e^ {2\pi i})^i = e^ { …

May 12, 2015 · The square root of i is (1 + i)/sqrt (2). [Try it out my multiplying it by itself.] It has no special notation beyond other complex numbers; in my discipline, at least, it comes up about …

Jan 12, 2015 · It is possible to interpret such expressions in many ways that can make sense. The question is, what properties do we want such an interpretation to have? $0^i = 0$ is a good …

As Will Jagy already pointed out, there is no accepted solution for this. There is a formal procedere which can sometimes lead to a meaningful/approximate answer; but this is then …

M Turgeon, thanks for that reference. The explanation there is a little beyond me but the example is great. I noticed that when you move the n back to the imaginary axis by factoring out the …

I can't seem to find a solution to this for the life of me. My mathematics teacher didn't know either. Edit: I asked the teacher that usually teaches my course today, and she said it was incredibl...

Oct 15, 2015 · We say that $X_1,X_2,...X_n$ are i.i.d random variables if they have identical distribution and are mutually independent, given probability space $(\\Omega, \\mathcal ...

It is defined that way. I believe the proper definition of i i is i2 = −1 i 2 = 1 and not i = −1−−−√ i = 1 as is commonly stated. It is useful in many deep areas of mathematics, but as a starting point, …