Felina wrote:37249
I was trying to figure out how would I imagine a function f(x) = x^2 + 1, since it has 2 imaginary zero points, i and -i. I mean, I know how it looks like in the real plain, but what about space?
So, 4D is a bit tough to imagine, so let's try 3D.
f: C --> R
to make that happen, you say that z = x + yi, and the function becomes
f(z) = z^2 + 1
BUT
you still have imaginary part of he f(z) and we're trying to put it in 3D so
f(x, y) = (x+yi)^2 + 1 - 2xyi
So, let's say you wanna make it look like it should in x-y plain, because that's just how we do stuff. x and y are therefore real axises and z is the imaginary one. (so, y is in fact z in the upper formula)
So, in x-y plain, it looks like a normal f: R-->R function as i should, and it touches z axis in i and -i.
It basically looks like two cool hills! So neat!
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