Complex numbers are just a field over 2D vectors, no? When you find "complex solutions to an equation", you're not working with a real equation anymore, you're working in C. I hate when people talk about complex zeroes like they're a "secret solution", because you're literally not talking about the same equation anymore.

There's this lack of rigor where people casually move "between" R and C as if a complex number without an imaginary component suddenly becomes a real number, and it's all because of this terrible "a + bi" notation. It's more like (a, b). You can't ever discard that second component, it's always there.

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petters 2 hours ago | parent | next [-]

We identify the real number 2 with the rational number 2 with the integer 2 with the natural number 2. It does not seem so strange to also identify the complex number 2 with those.

	▲	phailhaus an hour ago \| parent [-]
		If you say "this function f operates on the integers", you can't turn around and then go "ooh but it has solutions in the rationals!" No it doesn't, it doesn't exist in that space.

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creata 28 minutes ago | parent | prev [-]

I hate when people casually move "between" Q and Z as if a rational number with unit denominator suddenly becomes an integer, and it's all because of this terrible "a/b" notation. It's more like (a, b). You can't ever discard that second component, it's always there. ;)