A' = 23.956 + 7.291i
A has thus been incremented by 1.
Did you forget that complex numbers are basically vectors?
So if I work out the number of "bill counts" from 0 + 0i I guess that must be the bill count number thing you keep asking for and you have no infinity
So lets do it
0 + 0i = 0
0.956 + 0.291i = 1
1.912 + 0.582i = 2
2.868 + 0.873i = 3
....
22.944 + 6.984i = 24
hmmm not quite even so I guess
23 + 7i = 24.058577405857740585774058577406
Are you happy with Bill, I think I have followed your logic correctly?
Anyone else care to comment?
Hints: Bill count to 23 - 7i, -23 + 7i & -23 - 7i. Those are the obvious easy ones no maths required.
Clever ones will be able to mark all the co-ordinates for a bill count of 24.058577405857740585774058577406 and how many is that
If you haven't got it think circle centred on 0,0
So hopefully you all caught up so Bill says 24.058577405857740585774058577406 bill counts from the complex origin all you have to do is work out which of the infinite points on the circle of radius 24.058577405857740585774058577406 centred on 0,0 he means
In fact for any point you pick you can draw a circle 1 unit in size and those are the infinite number of values 1 bill count away depending on which of the infinite directions you decide to bill count. And you have no idea which way to count until your bill count is given to you as a proper complex number so you can get its direction from 0,0. This is dramatically different from real numbers where any number on has two numbers 1 bill count away.
So every complex number has infinite other complex numbers 1 bill count away and that doesn't even include all the complex numbers because we can see the circle doesn't pass thru every complex number. Good lord there is something therefore bigger than and more tricky than infinity then what shall we call it
Bill can write his bill count number using digits rather than a symbol is about the only difference I can see but I am sure Bill will clear this all up for me.
