Vectors and Complex Numbers

Abstract

A vector is a geometric object that has magnitude (or length) and direction and can be added to other vectors or multiplied by a scalar. Vectors play an important role in many branches of science, such as physics or engineering. They allow us to represent the position of objects in two, three or more dimensions and to store complex data having multiple components, such as velocity, temperature, pressure, etc. In this chapter we define vectors and their basic operations, such as addition, multiplication by a scalar, dot and cross products, together with some direct applications. The complex numbers in algebraic (vectors having one real and one imaginary component in the Argand diagram) and polar (vectors having radius and argument) form of are then presented, along with some of key operations and results.