Modulus of a Real Number

Absolute value discusses area from zero point without the consideration of direction. Absolute value of any number can never be negative. It is always positive. Alternatively, it can be stated that “modulus of real number” is described algebraically in a precise and meaningful manner or way. For instance, if a real number is not negative, the absolute value will not turn negative, it shall remain the same.

Concept of Real Number

Real numbers are mainly the amalgamation of both rational as well as irrational numbers, within the number system. In general, it can be stated that the “modulus of real number” in various numerical operations can be performed. This can be brought into representation also within a given number line. On the same grounds, it can be stated that numbers that are imaginary are said to be non-real numbers. As a result, this number, in general, cannot be expressed within line numbers.  It is generally used in the representation of a complex number.

“Modulus of real numbers” in general can be described as a complex combination of both the rational as well as irrational numbers. Rational numbers and irrational numbers can either be positive or negative by nature. However, it is denoted by a specific symbol named R . It can be said that every natural number, fraction and decimal all are covered within this category.

Properties of Real Number

Following are the basic properties of real numbers which are used in the determination of simplified mathematical expressions. 

 Closure Property- As per this property, it can be stated that “modulus of real number” is generally closed by sum, minus and multiply.

Commutative Property – It states that altering the order in summation or by multiplying real numbers does not change any kind of result. There is the presence of both summation and multiplication of commutative properties of “modulus of real number”.

Associative Property- This property further seeks that by altering or changing up the addition or multiplication or ”modulus of real number” do not change any such result.

Distributive Property- It can be stated that this property is generally applied when the students are found in simplifying numerical expressions by parenthesis. This is also known by the name of the property of multiplication. Further, it states for any real numbers x, y or z, the distributive property can be stated as x (y+z) = xy + yz.

How to find the modulus of a real number?

In order to understand the question “How to find the modulus of a real number” it can be answered in the following manner by stating that “modulus of real number” is described algebraically in a precise and meaningful manner or way. For instance, if a real number is not negative, the absolute value will not turn negative, it shall remain the same.

In a broader perspective, it can be stated that the modulus function of a real number by nature is not negative by nature. If f (z) is a function of “modulus of real number”, then it can be stated that there are basically three assumptions or conditions. Firstly, when z is positive, then f (z) = z. Secondly, when z is equal to zero, then f (z) = 0 and finally it can be stated that when the value of z is larger than 0, then the result is f (z) = -z.

Application of Modulus of real number

Let us consider a numerical illustration for understanding the application of modulus of a real number:

Example A. Solve (z+3) = 8 by using modulus real number function

Answer. As it is known that “modulus of real number” is not negative each time, it can be said that there are two cases of modulus real number function.

Assumption No. 1

When z+3 is greater than 0,

(z+3) = z+ 3

z+3 = 8

z= 8-3

z= 5

Assumption No. 2

When z+3 is lesser than 0,

{z+ 3} = – (z + 3)

– (z + 3) = 8

z= -3 -8

z= -11

Thus, the value of z can either be 5 or – 11.

Conclusion

It can be concluded from the above discussion that the absolute value of any number can be never negative. Absolute value discusses the area from zero point without the consideration of direction. The absolute value of any number can be never negative. It is always positive. Alternatively, it can be stated that the “modulus of real number” is described algebraically at a precise and meaningful manner or way. For instance, if a real number is not negative, the absolute value will not turn negative, it shall remain the same. In general, it can be stated that the “modulus of real number” in various numerical operations can be well performed.