I am having trouble getting the sympy.py solve function to produce an answer to this problem. The answer should be Q/q = 2*sqrt(2).
import sympy as sy
q,Q,a, K = sy.symbols('q Q a K')
F21 = K * q * Q / a**2 * (-sy.I)
F41i = K * Q * Q / (2*a**2) * 1/sy.sqrt(2) * (sy.I)
Eqn = (F21 + F41i)
print(Eqn)
ans = sy.solve(Eqn,Q/q)
print(ans)
If the ratio does not appear as a literal expression, you must make it do so before attempting to solve for it. A common way to do this is to replace the numerator in the ratio with a dummy variable multiplied by the denominator, e.g.
>>> solve(Eq(x, Q/q), Q) # x = Q/q -> Q = q*x
[q*x]
>>> solve(Eqn.subs(Q, _[0]), x)
[0, 2*sqrt(2)]