What you need to know
Check yourself against these “I can” statements.
- I can write a complex number in exponential form, re^(iθ)
- I can multiply and divide complex numbers in exponential form
- I can explain de Moivre's theorem and use it to find powers of complex numbers
- I can use de Moivre's theorem to prove trig identities and to sum series
- I can solve equations like z^(n) = a + ib, including z^(n) = 1
- I can use the complex nth roots of unity to solve geometry problems
Practise this topic
3 resourcesComplex Numbers Review (Year 2)
Multi-part exam-style questions reviewing Core Pure 2 complex numbers, with marks for each part: de Moivre’s theorem and exponential form (powers, proof by induction, roots), nth roots and geometry (roots on an Argand diagram…
🧮 ToolDe Moivre Explorer
Drag w on a large Argand diagram and see its n roots (n = 1 to 12) on a circle as a regular n-gon, with the angle 2π/n marked, the principal root, their sum (vectors head to tail) and conjugate pairs; the roots of unity with…
🧩 ConnectionsRoots of Complex Numbers
Each group is four roots of one equation zⁿ = w in modulus-argument, exponential or a + bi form. From Standard every equation in a puzzle has the same power and modulus, arguments are unsimplified or outside the principal range…
Topics in this unit
- 1.1 Exponential form of complex numbers · 2 resources
- 1.2 Multiplying and dividing complex numbers · 2 resources
- 1.3 De Moivre’s theorem · 2 resources
- 1.4 Trigonometric identities · 1 resource
- 1.5 Sums of series · 2 resources
- 1.6 nth roots of a complex number · 3 resources
These are the pages for Complex numbers in the A Level Further Maths scheme of work, following Pearson Edexcel A Level Further Mathematics (9FM0). Open this topic in Mr Wells Maths to see it alongside the rest of the course.