Complex Numbers

Complex numbers.

Complex numbers are a group of figures resulting from the sum between a real number and one imaginary guy. A real number, according to the d
efinition, is one that can be expressed by an integer or decimal number. Instead, an imaginary number is one whose square is negative. The concept of imaginary numbers was developed by Leonhard Euler in 1777, when he gave the name v-1 of i ("imaginary").
The notion of a complex number is the impossibility of real numbers to cover the roots of even order the set of negative numbers. Complex numbers can, therefore, reflect all roots of polynomials, something that the real numbers are not able to do.
The actual number of each body is formed of ordered pairs (a, b). The first component (a) is the real part, while the second component (b) is the imaginary part. The pure imaginary numbers are numbers that are only formed by the imaginary part (hence, a = 0).
Complex numbers form the body called complex (C). When the real is identified with the corresponding complex (a, 0), the body of these real numbers (R) component is converted into a subfield of C. Moreover, C forms a two-dimensional vector space over R. This shows that complex numbers do not support the ability to maintain order, unlike the real numbers.