Complex Numbers: Applications and Representations

This lecture by the instructor covers the origin of complex numbers, their role in solving cubic equations, and their applications in crystallography and materials science. It delves into the construction of complex numbers, their graphical representation, polar form, and exponential form. The lecture also explores the manipulation and relations in the complex plane, the graphical representation of complex numbers, and the exponential form for cosine and sine functions. Furthermore, it discusses the microscopic Maxwell's equations, propagation of waves in free space, and the reciprocal space and Bragg condition for X-rays probing crystal lattices.