Program, Semester Week 3

Complex Numbers

Complex numbers and elementary complex functions are important tools for engineers for solving mathematical problems and describing physical systems. Of that reason we dedicate this week and a bit of next week to the study of complex numbers. We will begin by defining the complex numbers and showing notation and arithmetic tools for working with them. First and foremost it is important that you practice fundamental calculations with complex numbers until they feel no different than when working with the usual real numbers.

Remark

The lectures in this week 3 and throughout the rest of the semester will be taught by Steeven H. Spangsdorf, part-time lecturer at DTU Compute.

Key Terms

Complex numbers as ordered number pairs. The elementary arithmetic operations on complex numbers: addition, subtraction, multiplication, and division. The imaginary unit \(i\). Rectangular form \(z=a+ib.\) Real part \(\mathrm{Re}(z)\) and imaginary \(\mathrm{Im}(z)\) part. The complex conjugate \(\bar z\). Absolute value of complex numbers. The fundamental sets of numbers: \(\,\mathbb N,\, \mathbb Z,\, \mathbb Q,\, \mathbb R\,\) and \(\,\mathbb C\) - complex numbers are considered a branch on the stem of numbers just like natural numbers, integers, rational numbers, and real numbers.

Preperation and Syllabus

This week will cover Sections 3.1 through 3.5 from Chapter [03 - Complex numbers].

Exercises

Exercises for Long Day.

Exercises for Short Day.