Anonymous at Thu, 9 May 2024 18:48:42 UTC No. 16167755

>>16167628
and it's beautiful.

Anonymous at Thu, 9 May 2024 18:49:51 UTC No. 16167757

>>16167628
Complex numbers are great. Try solving AC circuits without them

Anonymous at Thu, 9 May 2024 19:07:40 UTC No. 16167781

>>16167628
*maths

Anonymous at Thu, 9 May 2024 21:24:25 UTC No. 16167978

If you're introducing complex numbers, you're also adding a complex plane, so the circles are really spheres, thus intersect in complex plane. In the 2d xy plane you're seeing the projection as circles only where they don't touch

Anonymous at Thu, 9 May 2024 21:32:16 UTC No. 16167988

>>16167757
>introduces rotation as a linear transformation in [math] \mathbb R^2 [/math]

Anonymous at Fri, 10 May 2024 05:51:41 UTC No. 16168591

>>16167978
>so the circles are really spheres
Not at all. The equation x^2 +y^2 = r^2 for complex x and y doesn't look like a sphere. Its solution set contains values arbitrarily far away from then origin, i.e. is not bounded by r.

Anonymous at Fri, 10 May 2024 07:00:42 UTC No. 16168652

>>16167755
exactly
>>16167781
exactly
>>16168591
exactly

Anonymous at Fri, 10 May 2024 07:11:17 UTC No. 16168655

>>16167757
Gimme one ac circuit and I will show how to do it

Anonymous at Fri, 10 May 2024 07:32:53 UTC No. 16168668

>>16167628
The real circles don't intersect, but the complex circles do.

Anonymous at Fri, 10 May 2024 07:34:43 UTC No. 16168669

>>16168668
But they're not complex circles. See >>16168591. The equation for a complex circle would involve complex conjugates.

Anonymous at Fri, 10 May 2024 07:50:48 UTC No. 16168676

>>16168669
What is a complex circle, then?

Anonymous at Fri, 10 May 2024 08:13:49 UTC No. 16168690

>>16168676
Similar definition as a real circle but with hermitian instead of euclidean metric.

Anonymous at Fri, 10 May 2024 08:33:14 UTC No. 16168708

>>16167628

Trivia: This doesn't hold for surperimposed circles.
Not trivia: In the complex plane, these are hyperspheres.

I also wonder how many inetrsection points there are when one considers hypercomplex dimensions?

Anonymous at Fri, 10 May 2024 10:15:18 UTC No. 16168777

>>16167978
More like glomes: https://polytope.miraheze.org/wiki/Glome

Anonymous at Fri, 10 May 2024 13:14:21 UTC No. 16168943

>>16168655
A challenger appears, will anon provide an ac circuit?

Anonymous at Fri, 10 May 2024 13:40:39 UTC No. 16168967

Anonymous at Fri, 10 May 2024 13:43:21 UTC No. 16168970

>>16167628
go find the root(s) of a general cubic equation