From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 26 Feb 2019 11:03:09 +0000 (+1100)
Subject: [spec] 4f - conjugate root theorem
X-Git-Tag: yr12~235
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/2bdb56cc054e50902db582a91f20596bdb00872c?hp=d36d016eaa5cad131ca4e3b7443be9cc39e1bcdb

[spec] 4f - conjugate root theorem
---

diff --git a/spec/complex.md b/spec/complex.md
index d111921..959c241 100755
--- a/spec/complex.md
+++ b/spec/complex.md
@@ -110,6 +110,8 @@ $z^2+a^2=z^2-(ai)^2=(z+ai)(z-ai)$
 
 ## Solving complex polynomials
 
+Include $\pm$ for all solutions, including imaginary.
+
 #### Dividing complex polynomials
 
 Dividing $P(z)$ by $D(z)$ gives quotient $Q(z)$ and remainder $R(z)$ such that:
@@ -122,7 +124,7 @@ Let $\alpha \in \mathbb{C}$. Remainder of $P(z) \div (z - \alpha)$ is $P(\alpha)
 
 ## Conjugate root theorem
 
-Let $P(z)$ be a polynomial with real coefficients. If $a+bi$ is a solution to $P(z)=0$, with $a, b \in \mathbb{R}$, the the conjugate $a-bi$ is also a solution.
+If $a+bi$ is a solution to $P(z)=0$, with $a, b \in \mathbb{R}$, the the conjugate $a-bi$ is also a solution.
 
 ## Polar form