From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 4 Mar 2019 09:32:52 +0000 (+1100)
Subject: [spec] complex factor theorem
X-Git-Tag: yr12~225
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/7d1e263ffed78f8991751219a3f88aaee0f24b1a

[spec] complex factor theorem
---

diff --git a/spec/complex.md b/spec/complex.md
index ce71511..e72225e 100755
--- a/spec/complex.md
+++ b/spec/complex.md
@@ -128,6 +128,12 @@ $$P(z) = D(z)Q(z) + R(z)$$
 
 Let $\alpha \in \mathbb{C}$. Remainder of $P(z) \div (z - \alpha)$ is $P(\alpha)$
 
+#### Factor theorem
+If $a+bi$ is a solution to $P(z)=0$, then:
+
+- $P(a+bi)=0$
+- $z-(a+bi)$ is a factor of $P(z)$
+
 ## Conjugate root theorem
 
 If $a+bi$ is a solution to $P(z)=0$, with $a, b \in \mathbb{R}$, then the conjugate $\overline{z}=a-bi$ is also a solution.