[en] We present a new, simple way to estimate the rate of exponential growth (Lyapunov exponent) of solutions of the finite-difference Schroedinger equation: ((H-E)ψ)(n)=^def-[ψ(n+1)+ψ(n-1)]+[λf(αn+θ)]ψ(n). Here f is a non-constant real-analytic function of period 1 and α is irrational. For λ large we prove that the Lyapunov exponent is postitive for energy E in the spectrum of H and a.e. θ. In particular, the absolutely continuous spectrum of H is empty. In the continuum we study the quasi-periodic operator on L²(R) H= - d²/dx² - K²[cos x+cos(αx+θ] for large K and show that for wide intervals of low energies the Lyapunov exponent is positive. The main idea, which originated from M. Herman's subharmonic argument, is to deform the phase θ to the complex plane. This enables us to avoid small denominator problems by moving them off the axis, making estimates much easier to perform. We recover the information for real θ using an elementary extension of Jensen's formula (subharmonicity). (orig.)