Complex numbers are those that result from the sum of a real number and an imaginary number; being understood as a real number, one that can be expressed in an integer (s, 10, 300, etc.) or decimal (2.24; 3.10; etc.), while the imaginary is that number whose square is negative. Complex numbers are widely used in algebra and analysis, in addition to being applied in other specialties of pure mathematics such as the calculus of integrals, differential equations, in hydrodynamics, aerodynamics, among others.
In mathematics, these numbers represent a group that are considered as points on the plane and are known as the complex plane. This group includes real and imaginary numbers. A striking feature of these numbers is the fundamental theorem of algebra, which states that any algebraic equation of degree “n” will have specifically “n” complex solutions.
The concept of complex numbers arises from the impossibility of real numbers to include the roots of even order, of the group of negative numbers. Therefore, complex numbers have the ability to show all roots of polynomials, which real numbers cannot.
As already mentioned, complex numbers are often used in various branches of mathematics, physics and engineering, and thanks to their characteristics they have the ability to represent electromagnetic waves and electric current. In electronics and telecommunications, the use of complex numbers is common.
According to historical records, the Greek mathematician Heron of Alexandria was one of the first to propose the appearance of complex numbers, this due to the difficulties that arose when building a pyramid. But it was not until the seventeenth century that complex numbers began to occupy a significant place in science. It is important to note that at that time they were looking for formulas that would allow obtaining exact roots of the polynomials of level 2 and 3. Therefore, their interest was to find the real roots of the equations that were mentioned above, as well as to fight with the roots of negative figures.
Finally, if you want to analyze complex numbers geometrically, you need to use a complex plane; understanding this as a modified Cartesian plane where the real part is located on the abscissa axis, while the imaginary ones are located on the ordinate axis.
