2. Let Maths take you Further…
FP2 (MEI) Complex Numbers- Complex exponents and using complex numbers to sum Real series
Let Maths take you Further…

3. Complex exponents and using complex numbers to sum real series
Before you start:
• You need to have covered the chapter on complex numbers in Further Pure 1, and sections 1 and 2 of this chapter.
When you have finished… You should:
• Understand the definition ejθ = cosθ + jsinθ and hence the form
z = rejθ
• Be able to use de Moivre’s theorem to sum suitable series

4. Euler’s relation:
De Moivre:

7. Prove:

9. Summing series

12. Complex exponents and using complex numbers to sum real series
When you have finished… You should:
• Understand the definition ejθ = cosθ + jsinθ and hence the form z = rejθ
• Be able to use de Moivre’s theorem to sum suitable series

13. Independent study:
Using the MEI online resources complete the study plan for Complex Numbers 3: Exponent form
Do the online multiple choice test for this and submit your answers online.