Thread 16775580

What's Witty on about now? Is there really some sense in which a line and a circle always intersect each other, sometimes in real points or else in complex points? I've never heard of that but also I've had barely any schooling in complex numbers beyond "it's sqrt(-1) lmao".

>>16775580 (OP)
-1 has a square root mod p if 4 divides p-1.

>>16775580 (OP)
>if asymptotes and limits are misunderstood then circles touch lines

>>16775580 (OP)
Stop reading whoever the fuck wrote that shit.

Curves 'intersect' where there is a pair of values x,y that satisfies both of their equations. When you allow complex numbers then the equation of any line and the equation of any circle will have two points in common (except when there's only one but you still count it twice because it's still basically two points just on top of each other).

From a theoretical standpoint complex numbers are usually the correct context for things, but for real world applications they might not make sense and a circle and line might not intersect at all from that perspective. Also the type of graphs you learn to draw in high school can only show real solutions.

>>16775580 (OP)
>Now this statement, whether agreeing or disagreeing with the one which told is the solutions, certainly hasn’t its multiplicity.
Has anyone really been far even as decided to use even go want to do look more like?

>>16775580 (OP)
https://en.wikipedia.org/wiki/Circular_points_at_infinity