What is a Complex Number?

A complex number is a number having both real and imaginary parts that can be expressed in the form of a + bi, where a and b are real numbers and i is the imaginary part, which should satisfy the equation i² = −1. In complex number, a is the real part and b is the imaginary part of the complex number.           physics--28formula-book-29

Complex No Formula

Complex graphs

When visualizing complex functions, both a complex input and output are needed. Because each complex number is represented in two dimensions, visually graphing a complex function would require the perception of a four dimensional space, which is possible only in projections. Because of this, other ways of visualizing complex functions have been designed.

Properties-

Field structure

Algebraic characterization

Solutions of polynomial equations