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## #1 2012-04-07 13:03:56

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?

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## #2 2012-04-07 19:22:30

bob bundy
Registered: 2010-06-20
Posts: 8,354

### 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

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## #3 2012-05-02 12:28:27

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!

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