use example environment

src/1_complex_numbers.md

@@ -69,11 +69,11 @@ complex conjugate of $z_2$:
 $$\frac{z_1}{z_2} = \frac{z_1 z_2^*}{z_2 z_2^*} = \frac{(a_1 a_2 + b_1 b_2) + (-a_1 b_2 + a_2 b_1) {{\rm i}}}{a_2^2 + b_2^2}.$$
 Check this!
 
-**Example** 
-$$\begin{align} 
-\frac{1 + 2{\rm i}}{1 - 2{\rm i}} &= \frac{(1 + 2{\rm i})(1 + 2{\rm i})}{1^2 + 2^2} = \frac{1+8{\rm i} -4}{5}\\
-&= -\frac{3}{5} + {\rm i} \frac{8}{5}
-\end{align}$$
+!!! check Example:
+    $$\begin{align} 
+    \frac{1 + 2{\rm i}}{1 - 2{\rm i}} &= \frac{(1 + 2{\rm i})(1 + 2{\rm i})}{1^2 + 2^2} = \frac{1+8{\rm i} -4}{5}\\
+    & = -\frac{3}{5} + {\rm i} \frac{8}{5}
+    \end{align}$$
 
 ### Visualization: the complex plane
 
@@ -185,13 +185,13 @@ We see that during multiplication, the norm of the new number is the *product* o
 
 ![image](figures/complex_numbers_12_0.svg)
 
-**Example** Find all solutions solving $z^4 = 1$. 
+!!! check Example: Find all solutions solving $z^4 = 1$. 
 
-Of course, we know that $z = \pm 1$ are two solutions, but which other solutions are possible? We take a systematic approach:
-$$\begin{align} z = e^{{\rm i} \varphi} & \Rightarrow z^4 = e^{4{\rm i} \varphi} = 1 \\
-& \Leftrightarrow 4 \varphi = n 2 \pi \\
-& \Leftrightarrow \varphi = 0, \varphi = \frac{\pi}{2}, \varphi = -\frac{\pi}{2}, \varphi = \pi \\
-& \Leftrightarrow z = 1, z = i, z = -i, z = -1 \end{align}$$
+    Of course, we know that $z = \pm 1$ are two solutions, but which other solutions are possible? We take a systematic approach:
+    $$\begin{align} z = e^{{\rm i} \varphi} & \Rightarrow z^4 = e^{4{\rm i} \varphi} = 1 \\
+    & \Leftrightarrow 4 \varphi = n 2 \pi \\
+    & \Leftrightarrow \varphi = 0, \varphi = \frac{\pi}{2}, \varphi = -\frac{\pi}{2}, \varphi = \pi \\
+    & \Leftrightarrow z = 1, z = i, z = -i, z = -1 \end{align}$$
 
 ## Differentiation and integration