Day 1

Goal of the course:

Complex analysis:

Examples of the use of complex numbers in Physics:

  • Electrical and mechanical oscillating systems are described by functions with complex arguments.
  • QM wavefunction: Every point of space has a corresponding complex number describing the phase and amplitude of the wavefunction.
  • EM waves. Every point of space has a corresponding complex number describing the phase and amplitude of the electric field.
  • Quantum operators. For example, the Pauli Spin matrices.

In-class exercises

  • Sketch values of f(z) = (z-2)^2+2 in the Argand plane.
  • Use two different methods
  • Show the roots of z^4 = 1 on the Argand plane.
  • Use Euler's equation to express sin2θ in terms of sinθ and cosθ.