From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Wed, 27 Feb 2019 06:23:42 +0000 (+1100)
Subject: sketching complex graphs
X-Git-Tag: yr12~234
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/9de4a0c785d0bec4dcaebd628467d5cbc67d4c85?hp=2bdb56cc054e50902db582a91f20596bdb00872c

sketching complex graphs
---

diff --git a/spec/complex.md b/spec/complex.md
index 959c241..c5ad6be 100755
--- a/spec/complex.md
+++ b/spec/complex.md
@@ -158,4 +158,10 @@ $(r\operatorname{cis}\theta)^n=r^n\operatorname{cis}(n\theta)$ where $n \in \mat
 $n$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
+Same modulus for all solutions. Arguments are separated by ${2 \pi} \over n$
+
+## Sketching complex graphs
+
+- **Straight line:** $\operatorname{Re}(z) = c$ or $\operatorname{Im}(z) = c$ (perpendicular bisector) or $\operatorname{Arg}(z) = \theta$
+- **Circle:** $|z-z_1|^2 = c^2 |z_2+2|^2$ or $|z-(a + bi)| = c$
+- **Locus:** $\operatorname{Arg}(z) \lt \theta$