Regions of absolute stability

In the study of the stability of ODE-solvers it is interesting to visualize to region of absolute stability of a method. The region is a set in the complex plane where a function, characteristic of the method, has a modulus less than one.

Here are the functions (polynomials) of two well-known Runge-Kutta methods.

RKF45:  p(h) = 1 + h + h2 / 2 + h3 / 6 + h4 / 24 + h5 / 104

DOPRI(5, 4): p(h) = 1 + h + h2 / 2 + h3 / 6 + h4 / 24 + h5 / 120 + h6 / 600

Just to clarify: the set of interest is the set of complex h such that | p(h) | < 1.

Question  Visualize the regions (in the same plot) in a clear way. Do not use images or other tools that require a lot of computation.

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