Complex Numbers

Abstract

Complex number z is an ordered pair of real numbers (a, b), where $a,b\in \mathbb {R}$. The first number a is called the real part of the complex number $z=(a,b)$ and is denoted by symbol $\mathrm{Re}z$, while the second number of the pair b is called the imaginary part z and is denoted $\mathrm{Im}z$  [23]. A complex number of the form (a, 0), where the imaginary part is zero, is identified with the real number a, i. e. $(a,0)\equiv a$. This allows considering the set of all real numbers $\mathbb {R}$ as s subset of set of complex numbers $\mathbb {C}$.