The concept of complex numbers identifies the numbers which have both real numbers and imaginary numbers. An imaginary number makes a sum in a complex and points to the position of the number in the graph. The application of complex numbers has been seen in the polynomial equation where the real number is sufficient to make mathematical problems. As per the Cartesian plane equation, the phase of a complex number is used as a radian value. In a graph, the concept of complex numbers is used to identify the position of a particle with its axis. This complex number has a positive sign and when it changes to a real number, teh sign becomes negative.

## A Brief Explanation of Complex Number

The concept of complex numbers defines the number which is integrated between an imaginary number and a real number. Imaginary numbers make the sum in a complex form which has been used to solve different kinds of quadratic equations. The concept of complex numbers has a standard format where both real variables and imaginary numbers are included. An example of the concept of complex numbers is C= a+ib. In this equation, a, and b are the real numbers and i is the imaginary number. The value of a, and b has numerical variables where the imaginary number has no value in real life. It is possible to change a complex number into a real one by squaring the imaginary number. As an example, if i is an imaginary number of a complex number then after squaring this imaginary number, its value becomes -1 which means i²=-1. The concept of complex numbers is not a complicated number. This number is used to conduct different kinds of complex equations where the coordinate axis indicates the position of the particle. In graph theory, the concept is used to identify the geometric position of a point of a particle. This complex number is classified into four types that include zero complex number, imaginary complex number, purely imaginary complex number and purely real number. Zero complex numbers define that both real and imaginary numbers are zero. an imaginary complex number identifies the numbers where both real and imaginary numbers are present. a purely imaginary complex number means the value of the real number is zero; only the imaginary number stays in summation. Purely real numbers indicate only the real part where the imaginary value is zero. The phase of a complex number helps to identify the nature of a point.

## Application of Complex Number in the Mathematics

Application of complex numbers has been seen in the polynomial equation in mathematics as real does not use it in polynomial equations. In real life, the application of complex numbers is used to make a quadratic equation where the real number is pointed on the X-axis and the imaginary number is pointed at the Y-axis. In physics, the application of complex numbers is most used in signal processing, fluid dynamics, electromagnetism, quantum physics and vibration equations.

The phase of a complex number can be seen in mathematics in radian form based on the position of a geometrical position. Along with the complex number helps introduce the Cartesian, cylinder or spherical form of a point with its axis where the geometric position of a particle can be identified.

### Conclusion

Conclusively, important aspects that are related to complex numbers are demonstrated in this note. The definition of complex numbers has been explained and the application of complex numbers in mathematics is defined. Overall, it can explain that complex numbers are the sum of real numbers and imaginary numbers. Real numbers play a subfield in complex numbers. Various polynomial equations are constructed with the help of complex numbers. Real numbers are not used in the polynomial equation. The phase of the complex number is always a positive sign as it is considered for counting counterclockwise.