Math Is Fun Forum

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?