Algebra - Complex Numbers Leaving Cert Helpdesk 27 th September 2012.

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Algebra - Complex Numbers Leaving Cert Helpdesk 27 th September 2012

Why do we need Complex Numbers?

Where are Complex Numbers used? Electronic Engineering Aircraft Design Medicine Movie/Computer game graphics

Adding and Subtracting Complex Numbers Group the real parts together and group the imaginary parts together. Examples:

Multiplication of Complex Numbers

Examples of Multiplication

The Complex Conjugate

Example of Division

Dividing one Complex Number by Another

Examples of the use of Complex Numbers

Argand Diagram

Modulus of a Complex Number

Polar Form of a Complex Number

Converting a Complex Number to Polar Form

De Moivres Theorem

De Moivres Theorem – Ex. 1

De Moivres Theorem - Example 2

Roots of a Complex Number

Proof by Induction

Proving De Moivres Theorem by Induction

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