Update src/1_complex_numbers.md

src/1_complex_numbers.md

@@ -293,31 +293,28 @@ function help in re-deriving trigonometric identities.
     3.  $b/a$.
 
 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:] 
-        (a) Find the real and imaginary part of 
-        $$ \frac{1+ {\rm i}}{2+3{\rm i}}$$
-        (b) Evaluate $$\left| \frac{a+b\rm i}{a-b\rm i} \right|$$ 
-        for real $a$ and $b$.
-
-5.  [:sweat:] 
-        1.  For any given complex number $z$, we can take the inverse $\frac{1}{z}$. 
-        2.  Visualize taking the inverse in the complex plane. 
-        3.  What geometric operation does taking the inverse correspond to? 
-            (Hint: first consider what geometric operation $\frac{1}{z^*}$ corresponds to.)
-
-6.  [:grinning:]  
-        (a) Compute $$\frac{d}{dt} e^{{\rm i} (kx-\omega t)},$$
-        (b) calculate the real part of $$\int_0^\infty e^{-\gamma t  +\rm i \omega t} dt$$ 
-            ($k$, $x$, $\omega$, $t$ and $\gamma$ are real; $\gamma$ is positive).
-
-7.  [:smirk:] 
-        Compute 
-        $$\int_{0}^{\pi}\cos(x)\sin(2x)dx$$
-        by making use of the Euler identity.
+    1. $\rm i^{1/4}$, 
+    2. $\left(1+\rm i \sqrt{3}\right)^{1/2}$,
+    3. $\exp(2\rm i^3)$.
+
+3.  [:grinning:] Find the three 3rd roots of $1$ and ${\rm i}$ </br>
+    (i.e. all possible solutions to the equations $x^3 = 1$ and $x^3 = {\rm i}$, respectively).
+
+4.  [:grinning:] </br>
+    1. Find the real and imaginary part of $$ \frac{1+ {\rm i}}{2+3{\rm i}}$$
+    2. Evaluate $$\left| \frac{a+b\rm i}{a-b\rm i} \right|$$ for real $a$ and $b$.
+
+5.  [:sweat:] </br>
+    1.  For any given complex number $z$, we can take the inverse $\frac{1}{z}$. 
+    2.  Visualize taking the inverse in the complex plane. 
+    3.  What geometric operation does taking the inverse correspond to? 
+    (Hint: first consider what geometric operation $\frac{1}{z^*}$ corresponds to.)
+
+6.  [:grinning:]  </br>
+    1. Compute $$\frac{d}{dt} e^{{\rm i} (kx-\omega t)},$$
+    2. Calculate the real part of $$\int_0^\infty e^{-\gamma t  +\rm i \omega t} dt$$ 
+    ($k$, $x$, $\omega$, $t$ and $\gamma$ are real; $\gamma$ is positive).
+
+7.  [:smirk:] Compute by making use of the Euler identity.
+    $$\int_{0}^{\pi}\cos(x)\sin(2x)dx$$
+