Today we shall explore the algebraic rules of real numbers already known from high school. We will recap on the relevant rules and then look at how they unfold on the larger set of complex numbers. How is problem solving carried out when switching from a solely real to a complex context?
Properties of real numbers and of complex numbers. The hierarchy of the arithmetic rules. Brackets. Fractions. The square theorems. The Pythagorian Theorem. The quadratic formula. Absolute values. Number sets and their symbols.
The first semester of Advanced Engineering Mathematics 1 is a coherent course in **linear algebra** and **linear differential equations**. Complex numbers and elementary complex functions are an important part of the basis for this theory. Therefore the first few weeks of the course are dedicated to the study of complex numbers. Today we will introduce the complex numbers as a new set of numbers belonging to the well-known family of number sets and we will work out how to write a complex number in its so-called *rectangular form*.
First and foremost it is important to practise computations with complex numbers to become familiar with them so they won't be dreaded when they show up in future mathematical topics.
