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(complex) root of unity
01-16-2021, 03:40 PM
Post: #4
RE: (complex) root of unity
Assumed n is positive integer.

Cas> rootsOfOne(n) := e^(2*pi*i*range(n)/n)
Cas> rootsOfOne(3)

[1, 1/2*√3*i-1/2, -1/2*√3*i-1/2]

Cas> rootsOfz(z,n) := z^(1/n) * rootsOfOne(n)
Cas> approx(rootsOfz(3+4i, 3))

[ 1.62893714592 +0.520174502305*i,
−1.26495290636 +1.15061369838*i,
−0.363984239564-1.67078820069*i]

Cas> Ans .^ 3

[3.+4.*i, 3.+4.*i, 3.+4.*i]
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Messages In This Thread
(complex) root of unity - salvomic - 01-16-2021, 02:47 PM
RE: (complex) root of unity - rprosperi - 01-16-2021, 02:57 PM
RE: (complex) root of unity - salvomic - 01-16-2021, 03:53 PM
RE: (complex) root of unity - robmio - 01-16-2021, 03:24 PM
RE: (complex) root of unity - salvomic - 01-16-2021, 03:56 PM
RE: (complex) root of unity - Albert Chan - 01-16-2021 03:40 PM
RE: (complex) root of unity - salvomic - 01-16-2021, 03:58 PM
RE: (complex) root of unity - salvomic - 01-16-2021, 05:27 PM
RE: (complex) root of unity - robmio - 01-16-2021, 05:42 PM
RE: (complex) root of unity - robmio - 01-16-2021, 05:47 PM
RE: (complex) root of unity - salvomic - 01-16-2021, 06:02 PM
RE: (complex) root of unity - robmio - 01-16-2021, 06:12 PM
RE: (complex) root of unity - salvomic - 01-16-2021, 06:17 PM
RE: (complex) root of unity - robmio - 01-16-2021, 06:28 PM
RE: (complex) root of unity - salvomic - 01-16-2021, 06:37 PM
RE: (complex) root of unity - robmio - 01-16-2021, 06:40 PM
RE: (complex) root of unity - salvomic - 01-16-2021, 06:48 PM
RE: (complex) root of unity - Jon Higgins - 12-26-2021, 11:45 AM



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