Notations

A complex number is a number combination of a real and imaginary part. It can be written in the form of a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property of i ² = −1. Complex numbers are containing the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication.

Notation:

The set of all complex numbers is usually denoted with an imaginary and real part.
Complex numbers are usually written in the form of a and b.
The form is a + bi
From this part a and b are real numbers, and i is the imaginary part, which has the property i 2 = −1. The real number a is called as real part of the complex number, and the real number b is called as imaginary part.

For example:

4 + 3i is a complex number, with real part 4 and imaginary part 3. If z = a + bi, the real part a is denoted Re(z), and the imaginary part b is denoted as Im(z).
In some disciplines, the imaginary part i is instead written as j, so complex numbers are sometimes contain as a + bj or a + jb.

History of Mathematical Notation:

Below list shows history of mathematical symbols for list of symbols in history of mathematical notation:

• Beginning of notation
• Greek notation
• Chinese notation
• Indian notation
• Beginning of Arabic numerals
• North African notation
• Pre-calculus
• Calculus
• Euler