I need to solve the equation
z1^n + z2^n == 1
with the parametrisation
z1 = Exp[2 π k1] I Cos[θ - ξ]^(2/n)
z2 = Exp[2 π k1] I Sin[θ - ξ]^(2/n)
Under the following assumptions:
k1, k2 ∈ N
k1 >= 0
k2 <= n − 1
0 <= θ <= π/2
Abs[ξ] <= max ξ
n = 2
The end result would look something like this and the coordinates {x, y, z}
would end up as {Re[z1], Im[z1], Re[z2]}
As I have understood this has something to do with the Riemann sphere.
k2
is nowhere to be found in bothz1
andz2
)? Or go go ahead and add every relevant detail to the question itself. $\endgroup$