(E^(200 I k0) - 3 E^(600 I k0))/(-3 + E^(400 I k0)) = 1

In[33]:= NSolve[(E^(200 I k0) - 3 E^(600 I k0))/(-3 + E^(400 I k0)) == 1 
&& -0.05067731239 <= Re[ k0 ] <= 0.05067731239, k0]
Out[33]={{k0 -> -0.0429185 + 0. I}, {k0 -> -0.0314159}, {k0 -> -0.0199133 +  0. I}, 
{k0 -> -0.0115026 + 0. I}, {k0 -> 0.}, {k0 -> 0.0115026 + 0. I}, {k0 -> 0.0199133 + 0. I}, 
{k0 -> 0.0314159}, {k0 -> 0.0429185 + 0. I}}

 from sympy import Symbol, sin, cos, I, exp, pi, solve, Eq, simplify, nsolve, solveset, pprint, ImageSet
k0 = Symbol('k0')
fun = (exp(200*I*k0) - 3*exp(600*I*k0))/(exp(400*I*k0) - 3) - 1
froot = solveset(fun, k0)
pprint(froot)

  
>>> solveset((exp(200 * x * I) - 3 * exp(600 * x * I)) / (-3 + exp(400 * x * I)) - 1)
повисло