/sci/ - Let's say I have a number line which solves for x. - Science & Math

Anonymous

09/15/24(Sun)19:46:31 No.16382458

File: FirePotion.jpg (53 KB, 709x1016)

Anonymous 09/15/24(Sun)19:46:31 No.16382458 Archived

Let's say I have a number line which solves for x.
I solve an equation and I get a complex solution.
So now I can make an imaginary plane and I can solve my equation in terms of x and i.
Since i is just another dimension could I not just say that the numbers in terms of i are just the y coordinates in a Cartesian system?
For example couldn't 4x+5i become (4,5)?

Anonymous
09/15/24(Sun)19:59:58 No.16382466

Anonymous 09/15/24(Sun)19:59:58 No.16382466

Yes, but not in a conventional way. Define your system to not have a y and just use i instead.

Anonymous
09/15/24(Sun)20:05:48 No.16382471

Anonymous 09/15/24(Sun)20:05:48 No.16382471

>>16382466

But it can be seen as interchangeable. If I have complex solutions I need another plane, and I can arbitrarily designate that plane as a dimension.

Anonymous
09/16/24(Mon)16:46:50 No.16383795

Anonymous 09/16/24(Mon)16:46:50 No.16383795

>>16382471
The complex numbers have an algebraic structure imposed on them that cartesian coordinates do not.

Anonymous
09/16/24(Mon)19:40:02 No.16383946

Anonymous 09/16/24(Mon)19:40:02 No.16383946

>>16383795
Yeah, but if both forms are valid, i may be either algebraic or dimensional. If i has a dimensional interpretation, that could lead to new ideas in math and physics.

Anonymous
09/16/24(Mon)19:41:57 No.16383948

Anonymous 09/16/24(Mon)19:41:57 No.16383948

>>16383946

Like Poincare defined time as an i dimension.