Dive into a comprehensive 51-minute video lecture exploring the intricacies of Euler's formula and its profound implications in mathematics. Uncover the meaning behind the computation of e^(πi) through interactive demonstrations, Python code examples, and engaging visual animations. Follow along as the lecturer breaks down complex concepts, including the properties of exponential functions, the relationship between complex numbers and rotations, and the periodic nature of e^(iθ). Participate in live questions and gain insights into the "celebrity equation" e^(πi) + 1 = 0. Conclude with thought-provoking homework assignments to deepen your understanding of this fundamental mathematical concept.