Formelsammlung.tex

@@ -43,14 +43,13 @@
 \item
   $\mathbb{N}$ = natürliche Zahlen = \{1, 2, 3, \ldots{}\}
 \item
-  Z = ganze Zahlen = \{\ldots{}, -1, 0, 1, 2, \ldots{}\}
+  $\mathbb{Z}$ = ganze Zahlen = \{\ldots{}, -1, 0, 1, 2, \ldots{}\}
 \item
-  Q = rationale Zahlen, z.b. \(\frac{p}{q}\) (p, q \(\in\) Z)
+  $\mathbb{Q}$ = rationale Zahlen, z.b. \(\frac{p}{q}\) (p, q \(\in \mathbb{Z}\), q \(\neq\) 0)
 \item
-  R = reelle Zahlen, „alle Zahlen``, z.b. \(\pi\)
+  $\mathbb{R}$ = reelle Zahlen, „alle Zahlen``, z.b. \(\pi\)
 \item
-  C = komplexe Zahlen = \{a + ib \textbar{} i = \(\sqrt{- 1}\), a,b
+  $\mathbb{C}$ = komplexe Zahlen = \{a + ib \textbar{} i = \(\sqrt{- 1}\), a,b \(\in \mathbb{R}\) \}
-  \(\in\) R\}
 \end{itemize}
 
 \subsection{Binomische Formeln}\label{binomische-formeln}
@@ -449,7 +448,7 @@ $a = 0, b = 0 $   & $\varphi = 0^\circ $    &       $\varphi = 0 $       \\
 	\end{align*}
 	\begin{align*}
 	{ z }_{ 1 }\cdot { z }_{ 2 } & =\left| { z }_{ 1 } \right| \left( \cos { \left( { \varphi  }_{ 1 } \right)  } +\sin { \left( { \varphi  }_{ 1 } \right)  } i \right) \cdot \left| { z }_{ 2 } \right| \left( \cos { \left( { \varphi  }_{ 2 } \right)  } \cdot \sin { \left( { \varphi  }_{ 2 } \right)  } i \right) \\ 
-	& =\left| { z }_{ 1 } \right| \cdot \left| { z }_{ 2 } \right| \left( \cos { \left( { \varphi  }_{ 1 } \right) \cdot \cos { \left( { \varphi  }_{ 2 } \right)  }  } +\sin { \left( { \varphi  }_{ 1 } \right)  } \cdot \sin { \left( { \varphi  }_{ 2 } \right)  } i \right)
+	& =\left| { z }_{ 1 } \right| \cdot \left| { z }_{ 2 } \right| \left( \cos { \left( { \varphi  }_{ 1 } + { \varphi  }_{ 2 } \right)  } +\sin { \left( { \varphi  }_{ 1 } + { \varphi  }_{ 2 } \right)  } i \right)
 	\end{align*}
 	
 \textbf{Division}