1 files changed, 23 insertions, 0 deletions
diff --git a/pages/complex-analysis/one-complex-variable/basics.md b/pages/complex-analysis/one-complex-variable/basics.md
new file mode 100644
index 0000000..b30d18c
--- /dev/null
+++ b/pages/complex-analysis/one-complex-variable/basics.md
@@ -0,0 +1,23 @@
+---
+title: Basics
+parent: One Complex Variable
+grand_parent: Complex Analysis
+nav_order: 1
+# cspell:words
+---
+
+# {{ page.title }}
+
+{: .theorem }
+> {: #holomorphic-function-is-constant-if-derivative-vanishes }
+>
+> If the derivative of a holomorphic function vanishes
+> throughout a connected open subset of the complex plane,
+> then it must be constant on that set.
+>
+> More generally, if the derivative of a holomorphic function vanishes
+> throughout an open subset of the complex plane,
+> then it must be constant on any connected component of that set.
+
+{% proof %}
+{% endproof %}