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10 cards from this deck
Trigonometry and complex numbers
Modulus-argument form (or exponential form)
rn(cos(nθ)+isin(nθ))r^n(\cos(n\theta) + i \sin(n\theta))rn(cos(nθ)+isin(nθ))
rnr^nrn
nθn\thetanθ
r1/n(cosθ+2kπn+isinθ+2kπn)r^{1/n}\left(\cos \frac{\theta + 2k\pi}{n} + i \sin \frac{\theta + 2k\pi}{n}\right)r1/n(cosnθ+2kπ+isinnθ+2kπ)
nnn distinct roots
k=0,1,2,...,n−1k = 0, 1, 2, ..., n-1k=0,1,2,...,n−1
−8−8i-8-8i−8−8i
222, −1+i3-1+i\sqrt{3}−1+i3, −1−i3-1-i\sqrt{3}−1−i3
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