The rapid expansion of data-intensive workloads highlighted the inherent efficiency limits of traditional digital logic. To navigate these bottlenecks, wave-based analog computing has emerged as a disruptive paradigm that transfers the computational load from sequential logic gates to the spatial configuration of the physical medium. By leveraging wave–matter interactions within specifically engineered structures, these platforms enable ultrafast, passive, and high-efficiency signal processing. In these systems, computational logic is embedded within the scattering matrix, which dictates the transformation of incident wave ports into scattered outputs. However, the functional range of these architected materials is constrained by fundamental physical principles, specifically passivity and reciprocity. Because purely passive systems possess strictly contractive scattering matrices, they are incapable of signal amplification or executing mathematical functions that require eigenvalues greater than unity. To transcend these barriers without the use of active hardware, we introduce a strategy that bypasses the passivity constraint through complex frequency excitation. In contrast to standard harmonic steady-state signals, this method employs waveforms defined by exponentially growing or decaying temporal envelopes. We show that such temporal modulation enables a standard passive material to replicate the behavior of an active system, producing an "effective" energy gain. By strategically mapping the transfer function’s zeros within the complex plane, we can mathematically offset material losses or generate the "virtual gain" necessary for solving ill-posed inverse problems. This methodology significantly broadens the design horizons for analog computing, empowering passive metamaterials to execute sophisticated operations that were once considered impossible without external power. We provide a rigorous theoretical framework alongside numerical evidence, demonstrating the technique's efficacy in solving differential equations. Our results offer a transformative approach to the design of wave-based processors, effectively reconciling the simplicity of passive structural mechanics with the demanding requirements of active computation.