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Mathematics · Ch 2 — Complex Numbers

de Moivre's Theorem and its Applications

2.8

de Moivre's Theorem and its Applications

Abraham de Moivre (1667–1754) was one of the first mathematicians to use complex numbers in trigonometry. The formula that bears his name,

(cos⁡θ+isin⁡θ)n=cos⁡nθ+isin⁡nθ,(\cos\theta+i\sin\theta)^n=\cos n\theta+i\sin n\theta,

was instrumental in bringing trigonometry out of the realm of pure geometry and into the realm of algebra/analysis — a power of a trigonometric expression becomes, via this formula, a single trigonometric expression at a sca …

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← Previous · 2.7.2Q6 — If z=x+iy and arg((z-i)/(z+2))=dfracπ4, show that x²+y²+3x-3y+2=0.Next · 2.8.1 →de Moivre's Theorem