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# Complex Numbers

By M Bourne

## Chapter Contents

1. Basic Definitions of imaginary and complex numbers - and where they come from.

2. Basic Operations - adding, subtracting, multiplying and dividing complex numbers.

3. Graphical Representation of complex numbers.

4. Polar Form of complex numbers

5. Exponential Form of complex numbers

6. Products and Quotients - more multiplying and dividing Fractals are computer-generated art using complex numbers.
See more at: Fractals.

7. Powers and Roots of complex numbers

8. AC Circuit Definitions - an electronics application of complex numbers

9. Impedance and Phase Angle - using complex numbers in AC circuits

10. Reactance and Angular Velocity - important when creating alternating currents

12. Parallel AC Circuits with exercises

## 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.

### 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).