IMAGINARY AXIS
Definition Of Imaginary Axis
The line in the complex plane corresponding to zero real part i.e. R [Z] = 0 is called Imaginary Axis.
More About Imaginary Axis
Imaginary Axis is the y-axis of a complex plane or Argand diagram.
Video Examples: Developing the Imaginary Axis
Example of Imaginary Axis
From the above figure, the x-axis is known as the real axis whereas the y-axis is known as the imaginary axis.
Solved Example on Imaginary Axis
Ques: Identify the graph that represents the point P on the imaginary axis.
Choices:
A. Graph 2
B. Graph 3
C. Graph 1
D. None of the above
Correct Answer: B
Solution:
Step 1: On a complex plane or Argand diagram, y-axis represents the imaginary axis.
Step 2: From the graphs given above, Graph 3 represents the point P on the imaginary axis as the point P in Graph 1 and 2 is on the real axis.
Step 3: Hence Graph 3 represents the point P on the imaginary axis.
Quick Summary
- Imaginary axis is the y-axis of the complex plane.
- Points on the imaginary axis have the form bi, where b is a real number.
🍎 Teacher Insights
Use visual aids and interactive software to help students understand the complex plane and the location of complex numbers on the imaginary axis. Emphasize the relationship between the real and imaginary parts.🎓 Prerequisites
- Real Numbers
- Coordinate Plane
- Basic Algebra
Check Your Knowledge
Q1: Which of the following points lies on the imaginary axis?
Q2: If a complex number 'z' lies on the imaginary axis, what is its real part?
Frequently Asked Questions
Q: What does the imaginary axis represent?
A: It represents all complex numbers with a real part of zero.
Q: How is the imaginary axis related to the complex plane?
A: It forms the vertical axis of the complex plane, with the real axis forming the horizontal axis.