Fixed typos and style in exercises

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