# Complex Numbers

By M Bourne

## How Complex can Numbers Get?

What are **complex numbers **? What are they good for?

**Application: **You are designing a simple AC circuit and you need to know the voltage across different parts of the circuit.

Perhaps you need to know what AC voltage to apply to the circuit, given that the current in the circuit needs to be 10 A.

How do you do it? What do you need to know?

To solve this problem, you need to know about **complex numbers**. When you finish studying this section, you will know a lot about complex numbers and their applications.

[You can see how to solve this electronics problem starting at AC Circuit Definitions.]

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### Survival Tips

Before trying to study complex numbers, it's a good idea to go back over these topics:

Radicals (also called **surds**), especially Addition and Subtraction and Multiplication and
Division of surds.

Radians (an alternative way of measuring angles).

### Helpful Vocabulary

For a complete list of vocabulary in this section (this includes words you have met already and new words that you will learn in this section), go to:

The chapter begins with Basic Definitions »

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Chapter Contents

- Complex Numbers
- 1. Basic Definitions of Complex Numbers
- 2. Basic Operations in Complex Numbers
- 3. Graphical Representation of Complex Numbers
- 4. Polar Form of Complex Numbers
- Convert polar to rectangular using hand-held calculator
- Polar to Rectangular Online Calculator
- 5. Exponential Form of Complex Numbers
- 6. Products and Quotients of Complex Numbers
- 7. Powers and Roots of Complex Numbers
- 8. AC Circuit Definitions
- 9. Impedance and Phase Angle: Application of Complex Numbers
- 10. Reactance and Angular Velocity: Application of Complex Numbers
- 11. AC Circuit Exercises
- 12. Parallel AC Circuits
- Vocabulary
- Fractals