/sci/ - Science & Math

Hey /sci/, I am unsure what to do about the imaginary unit in the power for the Euler's number. For reference, I am calculating the Fast Fourier Transform (the DFT formula is shown there) via a computer program so I will have an imaginary unit expressed somehow in a class called Complex. The Complex class resembles the complex numbers used in the sequence of elements. However, I am unsure what to do about the imaginary unit that is outside of the Complex class (as in, the Euler's number is that - it is not a complex number... or will I have to make the result of the Euler's number ^ power a complex number? ...but then, what would I put down for the imaginary unit inside the Complex class?)

Sorry if I seem to be rambling here, I am not very good with imaginary units.

Hi, I'm not a retard when it comes to math but to... pages I would consider "poorly explained" I do become a retard. Fortunately, this only happens on what I consider "high level formulas". I'm looking at Fast Fourier Transform right now (pic is the formula).

What the fuck do I do with the following:

xn
i
k
n
N

I am simply trying to figure it out so I can calculate the FFT in a computer program, but if I do not understand how to implement the formula, I cannot create the program. The wikipedia page says nothing about the values I'd like to know how to use.

How do I get xn? I am wildly guessing that xn would be the same number as some Xk value, but how do I achieve that if n and k appear to have the same values?
What is i? If it is an imaginary number, how do I implement that in a computer program? Value of 1?
What is k? Why not call it n since it seems to be the same counter value?
What is n? Why not call it k since it seems to be the same counter value?
How do I decide N? Is it up to me to decide what number it is?

Thanks in advance, /sci/.