Week Program, Semester Week 3

Complex Numbers

Complex numbers and elementary complex functions are important tools for engineers. Of that reason the next two weeks of the course are dedicated to the study of complex numbers. Today we will define the complex numbers and show how we arrive at the usual notation for a complex number, called its rectangular form. First and foremost it is important to practice computations with complex numbers.

Key Terms

Complex numbers as ordered number pairs. The elementary arithmetic operations: Addition, subtraction, multiplication and division. The imaginary unit \(\,i\,\) and the rectangular form \(\,z=a+ib\,.\) Real part and imaginary part. Conjugated number. Absolute value of complex numbers. The number sets \(\,\mathbb N,\, \mathbb Z,\, \mathbb Q,\, \mathbb R\,\) and \(\,\mathbb C:\) Complex numbers are considered as a branch on the stem of natural numbers, integers, rational numbers and real numbers.

Preperation and Syllabus

This week covers sections 3.1 through 3.5 from [03 - Complex numbers].

Exercises

Exercises for Long Day

Exercises for Short Day