Why can't imaginary numbers make sense?
>>16945828Skill issue. They arise quite naturally when you try to extend the rational or real numbers. All it takes is:1. there is a set [math]\mathbb{S}\supset\mathbb{R}[/math] that forms a number field, this implies there is at least one new number in it, meaning [math]\exists x\in\mathbb{S}:x\not\in\mathbb{R}[/math]2. knowing only x and the reals, you can construct every element of [math]\mathbb{S}[/math] through arithmetic (addition, multiplication, division) in a limited number of steps. Turns out, that limited number can always be simplified to 2 and the only solution is the complex numbers.
>>16945860replacing x with any finite number of new numbers changes nothing, and all but one are gonna end up redundant.Complex numbers are pretty goddamn unique in that regard.
>>16945828Sqrt(-1) = iThere. You now understand imaginary numbers.
you don't need to understand.
>>16945828they do make sense, it's just the name that filters people
>>16945828Perhaps you lack the proper degree of imagination necessary to make sense of them in your own head.
>>16945828Skill issue.If you can't make sense of the imaginary unit there is no hope you can fathom the hyperbolic unit.[math]j^2=+1,\; j\notin\mathbb{R}[/math]
