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re
complex roots
author
Andrew Lorimer
<andrew@lorimer.id.au>
Mon, 25 Feb 2019 11:41:54 +0000
(22:41 +1100)
committer
Andrew Lorimer
<andrew@lorimer.id.au>
Mon, 25 Feb 2019 11:41:54 +0000
(22:41 +1100)
spec/complex.md
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b/spec/complex.md
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spec/complex.md
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spec/complex.md
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${z_1 \over z_2} = {r_1 \over r_2} \operatorname{cis}(\theta_1-\theta_2)$ (divid
## de Moivres' Theorem
$(r\operatorname{cis}\theta)^n=r^n\operatorname{cis}(n\theta)$ where $n \in \mathbb{Z}$
+
+## Roots of complex numbers
+
+$n$th roots of $r \operatorname{cis} \theta$ are:
+$z={r^{1 \over n}} \cdot (\cos ({{\theta + 2k \pi} \over n}) + i \sin ({{\theta + 2 k \pi} \over n}))$
+
+Same modulus for all solutions. Arguments are separated by ${2 \pi} \over n$
\ No newline at end of file