From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 25 Feb 2019 11:41:54 +0000 (+1100)
Subject: complex roots
X-Git-Tag: yr12~237
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/dfc1aecf3c2278e043617d2b60fa767b7f454fc8?ds=sidebyside

complex roots
---

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