Examples On Modulus Function: Definition, Graphical Representation & Important Questions

The modulus function, which is often known as the absolute value function, is a crucial mathematical notion that has applications across various domains. It describes a method for calculating a number's distance from zero on the number line, regardless of its sign. Studying the modulus function, its graphical representation and several instances of how it might be used in practice are necessary to clarify your conceptual knowledge.

What is Modulus Function?
Graphical Representation of Modulus Function
Examples On Modulus Function

What is Modulus Function?

The modulus function, denoted as |x|, defines the absolute value of a real number x. It represents the distance x from zero on the number line. The modulus function takes any real number as an argument and produces a non-negative result. Whether the input is positive or negative, the output is the same. If the input is negative, the modulus function cancels out the sign and returns a positive value. For instance, |3| equals 3, |0| equals zero, and |-5| equals 5.

Graphical Representation of Modulus Function

The modulus function is represented graphically by a V-shaped graph. The function is broken into two parts: positive and negative branches. The positive branch is shown by the line y = x above the x - axis, while the negative component is represented by the line y = - x below the x-axis. This symmetric graph shows how the modulus function, regardless of sign, represents the distance from zero of the input.

Graphical Representation of Modulus Function

Examples of Modulus Function

When studying Modulus Function, it is important to practice a few questions to make your concepts more clear. Here are some of the solved examples on modulus function you might find helpful.

Example 1: Find the distance between the points (-4, 2) and (3, -1) with the help of the modulus function.

Solution:

Now, applying this formula to the given points, we get

Therefore, the distance between the points (-4, 2) and (3, -1) is

Example 2: Simplify the expression

Solution:

Therefore, the expression simplifies to 9.

Example 3: Calculate the value of the modulus of the complex number 4 - 3i.

Solution:

The modulus of a complex number a + bi is given by

Solution: We have two cases for this situation.
Case 1:

FAQs

Q1. Is the modulus function applicable to complex numbers?
Ans. Yes, the modulus function applies to complex numbers. Complex numbers may be utilized to find out the absolute value of complex numbers. For any complex number a + bi, the value of the modulus of this number can be calculated using the formula

Q2. What role does the modulus function have in distance calculations?
Ans. To compute the distance between two points in the coordinate plane, we make use of the modulus function. It computes the absolute difference between the x and y coordinates, further giving accurate value. The formula for this is , where (x₁, y₁) and (x₂, y₂) are coordinates of the two points.

Q3. What is the result of applying the modulus function to zero?
Ans. When the modulus function is applied to zero, it returns zero. In other words, |0| = 0. Since zero is a null value, therefore, if any sign is also there, it won’t affect the outcome of this expression.