From 52cffc053a306195f5a69a4bfeb2fa3ddf4bf5ae Mon Sep 17 00:00:00 2001
From: Michael Wimmer <m.t.wimmer@tudelft.nl>
Date: Thu, 27 Aug 2020 07:18:49 +0000
Subject: [PATCH] Add first lecture video
---
src/1_complex_numbers.md | 8 +++++---
1 file changed, 5 insertions(+), 3 deletions(-)
diff --git a/src/1_complex_numbers.md b/src/1_complex_numbers.md
index 550cb46..070ef9d 100644
--- a/src/1_complex_numbers.md
+++ b/src/1_complex_numbers.md
@@ -6,6 +6,8 @@ title: Complex Numbers
## Definition and basic operations
+<iframe width="100%" src="https://www.youtube-nocookie.com/embed/fLMdaMuEp8s" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+
Complex numbers are numbers of the form $$z = a + b {\rm i}.$$ Here
$\rm i$ is the square root of -1: $${\rm i} = \sqrt{-1},$$ or,
equivalently: $${\rm i}^2 = -1.$$
@@ -65,7 +67,7 @@ $$\begin{align}
&= -\frac{3}{5} + {\rm i} \frac{8}{5}
\end{align}$$
-## The complex plane
+### Visualization: the complex plane
Complex numbers can be rendered on a two-dimensional (2D) plane, the
*complex plane*. This plane is spanned by two unit vectors, one
@@ -76,7 +78,7 @@ unit vector represents ${\rm i}$.
Note that the norm of $z$ is the length of this vector.
-### Addition in the complex plane
+#### Addition in the complex plane
Adding two numbers in the complex plane corresponds to adding the
horizontal and vertical components:
@@ -86,7 +88,7 @@ horizontal and vertical components:
We see that the sum is found as the diagonal of a parallelogram spanned
by the two numbers.
-### Argument and Norm
+### Argument and Norm in the complex plane
A complex number can be represented by two real numbers, $a$ and $b$
--
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