From dfc1aecf3c2278e043617d2b60fa767b7f454fc8 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Mon, 25 Feb 2019 22:41:54 +1100 Subject: [PATCH] complex roots --- spec/complex.md | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/spec/complex.md b/spec/complex.md index 871e1d4..d111921 100755 --- a/spec/complex.md +++ b/spec/complex.md @@ -150,3 +150,10 @@ ${z_1 \over z_2} = {r_1 \over r_2} \operatorname{cis}(\theta_1-\theta_2)$ (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 -- 2.47.1