IceBergSLiM
Lifer
- Jul 11, 2000
- 29,933
- 3
- 81
“The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete. The quaternions, being noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative.” - John Baez
In all the years I studied and worked on electronics I never used imaginary numbers when looking at circuits.
What the hell do you need it for?
As mentioned quaterions and don't forget octonions:
- Scalars are represented by 1 number.
- Complex numbers are represented by 2 numbers (1 real and 1 imaginary).
- Quaternions are represented by 4 numbers (1 real and 3 imaginary).
- Octonions are represented by 8 numbers (1 real and 7 imaginary).
...in the programming world, especially.
Outside of that, 'x' and 'n' are used more often.
-2 can be spilt into -1 and 2.. Sqrt of -1 = i and sqrt of 2.. Is well ... You know that..
lol...in the programming world, especially.
Outside of that, 'x' and 'n' are used more often.
The only thing about quaternions (and beyond) is that each imaginary number is equivalent to i anyway... so it's only really one number, but imaginary, so it's not.
In all the years I studied and worked on electronics I never used imaginary numbers when looking at circuits.
What the hell do you need it for?
Are -1 2 and -2 different numbers? I think so
It's used on anything that is not linear. In other words, anything that is not a steady DC circuit.
In circuits, it is used for the transient response. In DC, we do not care about the transient because it eventually hits steady state so quickly. If you do anything analog, you need to know imaginary numbers.
How can -1 * 2 and -2 be different?
As mentioned quaterions and don't forget octonions:
- Scalars are represented by 1 number.
- Complex numbers are represented by 2 numbers (1 real and 1 imaginary).
- Quaternions are represented by 4 numbers (1 real and 3 imaginary).
- Octonions are represented by 8 numbers (1 real and 7 imaginary).
Not necessary, only because it is pretty much the de facto standard taught in school. You can definitely do all that sine addition without using complex numbers, it's just more aggravating. This has more to do with Euler's identity than the claim that "i=sqrt(-1)," which, by itself, is kind of useless.