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3. Graphical Representation of Complex Numbers

by M. Bourne

We can represent complex numbers in the complex plane.

We use the horizontal axis for the real part and the vertical axis for the imaginary part.

 

Example:

The number 3 + 2j is represented by:

A is the representation of the complex number 3 + 2j.

Adding Complex Numbers Graphically

We can add complex numbers graphically. [This is the same idea as adding vectors graphically. See more at Adding 2D Vectors]

 

Example:

Add 1 + 2j and 3 - j graphically.

Answer:

We add the complex numbers by setting up a parallelogram. The solution is (4 + j).

 

Exercise

Perform graphically: (3 - 2j) + (-1 - j)

Answer:

The answer is 2 − 3j.

 

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Chapter Contents

• Complex Numbers
• 1. Basic Definitions
• 2. Basic Operations
• 3. Graphical Representation
• 4. Polar Form
• 5. Exponential Form
• 6. Products and Quotients
• 7. Powers and Roots
• 8. AC Circuit Definitions
• 9. Impedance and Phase Angle
• 10. Reactance and Angular Velocity
• 11. AC Circuit Exercises
• 12. Parallel AC Circuits
• Vocabulary
• Fractals

• Comments, Questions?

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