Harmonic Oscillator: Complex Numbers and Solutions

This lecture covers the introduction of complex numbers, their addition, multiplication, conjugation, and norm. It then delves into mathematical reminders such as derivatives and the Moivre's formula. The lecture proceeds to discuss the damped harmonic oscillator, presenting the method to find solutions and the different regimes based on the damping factor and the natural frequency. The solutions are expressed in terms of exponential functions and trigonometric functions. The lecture concludes with an illustration of the damped harmonic oscillator in the regime of weak damping.