Let Maths take you Further… FP2 (MEI) Complex Numbers: part 1 Polar form, multiplication in the Argand diagram, De Moivre’s theorem & applications Let Maths take you Further…

The polar form of complex numbers and De Moivre’s theorem Before you start: You need to have covered the chapter on complex numbers in Further Pure 1. When you have finished… You should: Understand the polar (modulus-argument) form of a complex number, and the definition of modulus, argument Be able to multiply and divide complex numbers in polar form Appreciate the effect in the Argand diagram of multiplication by a complex number Understand de Moivre's theorem

Recap

Recap

Multiplication in the Argand Diagram

Division in the Argand Diagram

De Moivre’s Theorem

Examples

Applications

Applications

Example

The polar form of complex numbers and De Moivre’s theorem Now you have finished… You should: Understand the polar (modulus-argument) form of a complex number, and the definition of modulus, argument Be able to multiply and divide complex numbers in polar form Appreciate the effect in the Argand diagram of multiplication by a complex number Understand de Moivre's theorem

Independent study: Using the MEI online resources complete the study plans for the two sections: Complex Numbers 1 & 2 Do the online multiple choice tests for these sections and submit your answers online.