IMAGINARY PART
Definition Of Imaginary Part
If z = x + iy is a complex number, then y is called the Imaginary Part of the complex number z.
More About Imaginary Part
The imaginary part of a complex conjugate is opposite to the sign of the imaginary part of that complex number.
If z is a complex number and zĂ⌠is its conjugate complex, then the imaginary part of z is given by 
.
Video Examples: Finding Real and Imaginary Parts
Example of Imaginary Part
The imaginary part of a complex number 3 - 4i is - 4.
Solved Example on Imaginary Part
Ques: Choose the imaginary part of the complex number 7 + 8i.
Choices:
A. 8i
B. - 7
C. 7
D. 8
Correct Answer: D
Solution:
Step 1: The imaginary part of the complex number 7 + 8i is 8.
[The imaginary part of the complex number a + ib is b.]
Quick Summary
- The imaginary part of a complex number z = x + iy is y.
- It's the coefficient of the imaginary unit 'i'.
- The imaginary part is a real number.
đ Teacher Insights
Emphasize that the imaginary part is the coefficient of 'i' and is a real number. Use visual aids like the complex plane to illustrate the real and imaginary parts.đ Prerequisites
- Real Numbers
- Basic Algebra
- Complex Numbers Basics
Check Your Knowledge
Q1: What is the imaginary part of the complex number 2 + 5i?
Q2: What is the imaginary part of the complex number -7 - i?
Q3: What is the imaginary part of the complex number 9?
Frequently Asked Questions
Q: What is the imaginary part of 5 - 3i?
A: The imaginary part is -3.
Q: Is the imaginary part an imaginary number?
A: No, the imaginary part is a real number.
Q: What is the imaginary part of a real number (e.g., 7)?
A: The imaginary part of a real number is 0.