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Anonymous at Sun, 15 Sep 2024 23:46:31 UTC No. 16382458
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 at Sun, 15 Sep 2024 23:59:58 UTC No. 16382466
Yes, but not in a conventional way. Define your system to not have a y and just use i instead.
Anonymous at Mon, 16 Sep 2024 00:05:48 UTC 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 at Mon, 16 Sep 2024 20:46:50 UTC No. 16383795
>>16382471
The complex numbers have an algebraic structure imposed on them that cartesian coordinates do not.
Anonymous at Mon, 16 Sep 2024 23:40:02 UTC 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 at Mon, 16 Sep 2024 23:41:57 UTC No. 16383948
>>16383946
Like Poincare defined time as an i dimension.