Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
- No direct alignment recorded
New NZC (2026)
NZC26-P4-NUM-NSO-K-Y10-01
Resources
- No external resource is currently specified.
Terminology
- De Moivre's theorem
- Polar form
- Modulus
- Argument
- nth root
- Roots of unity
- Argand diagram
Task goals
- Foundation: Convert a complex number between rectangular (a+bi) form and polar (modulus-argument) form, and state De Moivre's theorem for integer powers.
- Proficient: Apply De Moivre's theorem to compute a given integer power of a complex number expressed in polar form, simplifying the result back to rectangular form where required.
- Excellence: Use De Moivre's theorem to find all n distinct nth roots of a complex number (including roots of unity) and represent them on an Argand diagram, or use the theorem to derive a trigonometric multiple-angle identity.
Where this fits
What leads into this objective, and where it goes next.
Before
Irrational numbers
You are here
De Moivre's Theorem: Powers and Roots of Complex Numbers
Next
Year 10 is the last year of this phase — the curriculum lists nothing after this. No extension resources on the site yet.
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.