A Short Note on Complex Number Geometrical Representation

Complex numbers are the numbers with the formation, a+ib, where ‘i’ is the intermediate that satisfies the equation, i²=-1. Complex numbers are numbers that have two parts that are real numbers, and imaginary numbers. Complex numbers are a very important topic in mathematics, physics and any other topics related to applied science. The complex numbers take place, especially in algebraic equations of any topic. Therefore, any imaginary number or real number is always considered a complex number. These are especially applicable in electromagnetism and electronics. Any standard formation of any operation as a complex number can be represented in a graph and the presentation is called the geometrical representation of an equation.

Discussion on the Geometrical Representation of an Equation

The standard formation of a complex number to use in a geometrical representation of an equation is a+ib. The part ‘a’ of the standard formation of a complex number is the real part, ‘b’ is the imaginary part and ‘i’ is the imaginary unit. The imaginary unit always has a constant value and that is√-1. Thus, the equation consisted of the standard formation of a complex number that can be represented in a geometric graph. It can be done by putting the value of the part ‘a’ on the X-axis and the value of ‘b’ on the Y-axis. The plane on which the complex number is represented is known as the Complex Plane and is prevailed by C. The X and Y-axis divide the geometric chart into four parts and the parts are known as Quadrant- (I, II, III & IV) respectively. 

Geometrical representation of an Equation on Gaussian Plane

The distance from the ‘O’ point to the destination point is known as the modulus of that complex number. The ways to put the equation on a complex plane are as follows:

• Taking the equation into the standard form of a complex number is the first thing to do.

• Then, one has to identify the imaginary and the real part of the number.

• Thereafter, the point has to be moved to the X-axis according to the value of the real part.

• Moreover, the destination point has to be moved again from the last stage on the real axis parallel to the Y-axis, depending on the value of the imaginary part.

• Therefore, the final placement of the point is represented and the geometrical representation of the linear equation is considered as done.

Geometrical Representation of Linear Equation

The placement point, (x,y), of a complex number, has to be calculated first to put the value on the geometric graph. Therefore, the complex number has to be represented on the complex plane. It makes a right-angled triangle with the X and Y-axis of the chart of the geometrical representation of an equation. The Geometrical Representation of the Linear Equation of two variables usually gives a straight line on the graphical plane. The Geometric representation example of a linear equation is–

x x+22yy = 66

This gives us the possible values of x and y and using those values, a Geometrical Representation of a Linear Equation can be represented. This equation gives the following values of x and y: (x,y)=(0,3),(2,2),(4,1),(6,0). Putting these values on the graphical chart gives a straight line that forms a right-angled triangle with the X and Y-axis.

Conclusion

Learning the geometrical representation of an equation is very important for students. Some of the information in the biological processes is very complicated. These can be represented understandably and easily on a graph model. The representation of the counting of white blood cells is a Geometric representation example. The geometrical representation of an equation gives a proper idea according to the ranges of the counting of WBC. Another Geometric representation example is representing the equations of electronics on the Gaussian plane. Thus, it can be said that the geometrical representation of an equation is important in every aspect of the areas of science.