Table of Contents

# Day 1

### 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.