MODULUS OF A COMPLEX NUMBER
Definition Of Modulus Of A Complex Number
Modulus of a Complex Number is the distance of the complex number from the origin in a complex plane. The modulus | Z | of a complex number Z = x + iy is given by 
.
More About Modulus of a Complex Number
Modulus is also called as Absolute Value.
Modulus of a Complex Number Z is also denoted as mod Z.
Modulus| Z | of a complex number Z is also given as 
, where 
is the conjugate complex of Z.
Examples of Modulus of a Complex Number
The modulus of complex number 3 + 4i is given as | 3 + 4i | = 
= 
= 
= 5.
Video Examples: Complex Numbers : finding the modulus and argument
Solved Example on Modulus of a Complex Number
Ques: Find the modulus of the complex number 18 + 24i.
Choices:
A. 18
B. 30
C. 24
D. 42
Correct Answer: B
Solution:
Step 1: Modulus of the complex number 18 + 24i is | 18 + 24i | = = 900 = 30.
Quick Summary
- The modulus represents the absolute value or magnitude of the complex number.
- It's the distance from the origin to the point representing the complex number in the complex plane.
- It is always a non-negative real number.
🍎 Teacher Insights
Emphasize the geometric interpretation of the modulus as a distance. Use visual aids like the complex plane to illustrate the concept. Relate the modulus to the Pythagorean theorem.🎓 Prerequisites
- Real Numbers
- Imaginary Numbers
- Complex Plane
- Pythagorean Theorem
Check Your Knowledge
Q1: What is the modulus of the complex number 3 + 4i?
Q2: What is the modulus of the complex number 18 + 24i?
Frequently Asked Questions
Q: What is the modulus of a complex number?
A: The modulus of a complex number is its distance from the origin in the complex plane. It is also known as the absolute value.
Q: How do you calculate the modulus of a complex number?
A: For a complex number z = x + iy, the modulus |z| is calculated as sqrt(x^2 + y^2).