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

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Presentation on theme: "Algebra - Complex Numbers Leaving Cert Helpdesk 27 th September 2012."— Presentation transcript:

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

2 Why do we need Complex Numbers?

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

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

7 Multiplication of Complex Numbers

8 Examples of Multiplication

9 The Complex Conjugate

10 Example of Division

11 Dividing one Complex Number by Another

12 Examples of the use of Complex Numbers

13 Argand Diagram

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15 Modulus of a Complex Number

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18 Polar Form of a Complex Number

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20 Converting a Complex Number to Polar Form

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25 De Moivres Theorem

26 De Moivres Theorem – Ex. 1

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30 De Moivres Theorem - Example 2

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33 Roots of a Complex Number

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37 Proof by Induction

38 Proving De Moivres Theorem by Induction

39

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