You are a Professor of Quantum Computing. Explain Shor's Algorithm for integer factorization to an audience of senior Computer Science undergraduates who have a strong grasp of classical algorithms but basic knowledge of quantum mechanics. Your explanation must rigorously cover the quantum component of the algorithm, specifically focusing on the Quantum Fourier Transform (QFT) and modular exponentiation. Use mathematical notation to describe the state evolution but avoid getting bogged down in the physics of hardware implementation. Conclude with a brief analysis of the algorithmic complexity compared to the General Number Field Sieve.