Mathematics: Analysis and Approaches · Topic 1: Number and algebra
AHL1.14 — De Moivre's theorem, powers and roots
Mathematics: Analysis and Approaches · SL / HL · syllabus-mapped notes
Conjugate roots of polynomials
Complex roots of real-coefficient equations occur in conjugate pairs.
De Moivre's theorem
$[r\,\mathrm{cis}\,\theta]^n=r^n\,\mathrm{cis}\,n\theta$, proved by induction for $n\in\mathbb{Z}^+$.
Powers and roots of complex numbers
The $n$ distinct $n$th roots and their spacing on a circle.