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Algebra - Complex Numbers Leaving Cert Helpdesk 27 th September 2012

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Why do we need Complex Numbers?

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

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

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Multiplication of Complex Numbers

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Examples of Multiplication

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The Complex Conjugate

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Example of Division

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Dividing one Complex Number by Another

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Examples of the use of Complex Numbers

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Argand Diagram

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Modulus of a Complex Number

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Polar Form of a Complex Number

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Converting a Complex Number to Polar Form

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De Moivres Theorem

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De Moivres Theorem – Ex. 1

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De Moivres Theorem - Example 2

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Roots of a Complex Number

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Proof by Induction

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Proving De Moivres Theorem by Induction

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