A First Course in Complex Analysis
The real numbers have many nice properties. There are operations such as addition, subtraction, multiplication as well as division by any real number except zero. There are useful laws that govern these operations such as the commutative and distributive laws. You can also take limits and do calculus.
In the next section we show exactly how the complex numbers are set up and in the rest of this chapter we will explore the properties of the complex numbers. These properties will be both algebraic properties (such as the commutative and distributive properties mentioned already) and also geometric properties. You will see, for example, that multiplication can be described geometrically. In the rest of the book, the calculus of complex numbers will be built on the properties that we develop in this chapter.