Math Is Fun Forum

amIaware

Member

Registered: 2012-04-07

Posts: 1

Imagine complex solutions to circle where both x and y can be complex?

1)  I am wondering what the complex solutions to a unit circle would look like if both the x and y axes were
allowed to be complex? 
2) Does this question even makes enough sence to ask? 
3) Would there be 3 or 4 spatial dimentions in the solutions?
4) Would the unit circle drawn on complex x and y axes follow the  x^2 + y^2 = 1 or y= +or-sqroot(1-x^2) or
something else?   This is just basic equation for unit circle given usual x and y axes.
5) Some Real solutions of x,y pairs might be the usual (0, +or-1), (1/2, + or- sqroot(3)/2), (1,0), (1/sqroot2, +or-1/(sqroot2)).
6) Some Imaginary/Complex solutions of x,y pairs might be (2, +or-sqroot(-3)=+or-sqroot3i), and (sqroot(3)i, +or-sqroot(2)i).

Thanks for any help and hopefully this is posted in correct forum?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Imagine complex solutions to circle where both x and y can be complex?

hi amIaware

Welcome to the forum! 

I think you need to be able to visualise in 4D for this.

You're not a multi-dimensional, pan-galactic being by any chance?

Humans generally have trouble visualising this.

Your values are good though.

One solution offered a while back is to visualise in n dimensions first, and then let n = 4. 

Bob

ps.  Decartes had an idea that may help with your choice of username 'amIaware'.

He said "I think, therefore I am."

Well, you're certainly thinking .........

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Sumasoltin

Member

Registered: 2012-04-28

Posts: 30

Re: Imagine complex solutions to circle where both x and y can be complex?

Interesting idea!
Let's use a 4d space now: x,y,p,q
by (x pi) 0…5 (y qi) 0…5=1
we got x 0…5 y 0…5-p 0…5 q 0…5=1 and xp yq=0
{x 0…5 y 0…5-(1 x 0…5/y 0…5)p 0…5=1,q=xp/y}
We can't see it directly, so just plot z 0…5=x 0…5y 0…5 y 6­6-y 0…5/(x 0…5 y 0…5) and use your imagination!