From 44e492c59126700d02bb60c4c3164915dedf8c23 Mon Sep 17 00:00:00 2001
From: Timo1104 <t.r.vanabswoude@student.tudelft.nl>
Date: Mon, 10 Aug 2020 09:46:36 +0000
Subject: [PATCH] Fixed typos and style in exercises
---
src/1_complex_numbers.md | 12 ++++++------
1 file changed, 6 insertions(+), 6 deletions(-)
diff --git a/src/1_complex_numbers.md b/src/1_complex_numbers.md
index 3ec9d2b..b8a499b 100644
--- a/src/1_complex_numbers.md
+++ b/src/1_complex_numbers.md
@@ -257,22 +257,22 @@ function helps in re-deriving trigonometric identities.
1. [:grinning:] Given $a=1+2\rm i$ and $b=4-2\rm i$, calculate and draw in the
complex plane the numbers $a+b$, $a-b$, $ab$, and $a/b$.
-2. [:grinning:] Evaluate (i) $\rm i^{1/4}$, (ii)
- $\left(-1+\rm i \sqrt{3}\right)^{1/2}$, (iii) $\exp(2\rm i^3)$.
+2. [:grinning:] Evaluate (a) $\rm i^{1/4}$, (b)
+ $\left(-1+\rm i \sqrt{3}\right)^{1/2}$, (c) $\exp(2\rm i^3)$.
3. [:grinning:] Find the three 3rd roots of $1$ and ${\rm i}$ (i.e. all possible solutions to the equations $x^3 = 1$ and $x^3 = {\rm i}$, respectively).
-4. [:grinning:] Find the real and imaginary part of
+4. [:grinning:] (a) Find the real and imaginary part of
$$ \frac{1+ {\rm i}}{2+3{\rm i}}$$
- Evaluate $$\left| \frac{a+b\rm i}{a-b\rm i} \right|$$
+ (b) Evaluate $$\left| \frac{a+b\rm i}{a-b\rm i} \right|$$
for real $a$ and $b$.
-5. [:sweat:] For any given complex number $z$, we can take the inverse $\frac{1}{z}$. Visualize taking the inverse in the complex plane. What geomtric operation does taking the inverse correspond to? (Hing: first consider what geometric operation $\frac{1}{z^*}$ corresponds to.)
+5. [:sweat:] For any given complex number $z$, we can take the inverse $\frac{1}{z}$. Visualize taking the inverse in the complex plane. What geomtric operation does taking the inverse correspond to? (Hint: first consider what geometric operation $\frac{1}{z^*}$ corresponds to.)
6. [:grinning:] Compute (a)
$$\frac{d}{dt} e^{{\rm i} (kx-\omega t)},$$
and (b) calculate the real part of
- $\int_0^\infty e^{-\gamma t +\rm i \omega t} dt$ ($k$, $x$, $\omega$, $t$ and
+ $$\int_0^\infty e^{-\gamma t +\rm i \omega t} dt$$($k$, $x$, $\omega$, $t$ and
$\gamma$ are real; $\gamma$ is positive).
7. [:smirk:] Compute
--
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