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**amIaware****Member**- Registered: 2012-04-07
- Posts: 1

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,787

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 .........

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Sumasoltin****Member**- Registered: 2012-04-28
- Posts: 30

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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