A

Author: if-loop69420

notes/20240910112146.md

@@ -5,4 +5,4 @@ The complex numbers can thus be defined as $\mathbb{C} = \R + i | i = \sqrt{-1}$
 
 A complex number is always made up of two parts $z = a + i*b | a,b \in \R$ where a is called the real part and b is called the imaginary part.
 
-#math #numbers
+#math #numbers #complexNumbers

notes/20240910113001.md

@@ -12,4 +12,4 @@ $a = r \cos \varphi, b = r \sin \varphi$
 or
 $r^2 = a^2 + b^2, tan \varphi = \frac{b}{a}$
 
-#numbers #math
+#numbers #math #complexNumbers

notes/20240910114541.md

@@ -31,4 +31,4 @@ What is really nice about complex numbers is solving square roots.
 When looking at a complex number $z = [R, \psi]$, because of the rules for multiplication the complex number $w = [\sqrt{R}, \frac{\psi}{2}]$ 
 fills the condition $w^2=z$ or $w = \sqrt{z}$. This means when searching the n-th root of a number $w_j = [\sqrt[n]{R}, \frac{\psi}{n}+ \frac{2 \pi j }{n}], j \in \{0,1..., n-1\}$
 
-#math #rules #numbers
+#math #rules #numbers #complexNumbers

notes/20240910122857.md

@@ -2,4 +2,4 @@
 A conjugated complex number [[20240910112146]] is a complex number.
 If $z=a + ib$ then the conjugated complex number $\overline{z}=a-ib$
 
-#math #numbers
+#math #numbers #complexNumbers

notes/20240910123008.md

@@ -2,4 +2,4 @@
 [[20240910112146]]
 $z*\overline{z} = |z|^2$
 
-#conjugated #math #numbers
+#math #numbers #complexNumbers

notes/20240910125959.md

@@ -8,4 +8,4 @@ Quadratic equations can also be expressed as $z^2 + pz + q = (z-z_1)(z-z_2)$.
 When comparing the coefficients of the potencies of z you receive vieta's root theorem:
 $p = -(z_1 + z_2), q=z_1 z_2$
 
-#math #numbers #quadraticequations
+#math #numbers #quadraticequations #complexNumbers

notes/20241010155926.md

@@ -3,4 +3,4 @@ Like with real numbers [[20240910111450]] the quadratic equation with complex nu
 What is different to the real numbers is, that we no longer care about the sign of the expression under the root.
 If it is negative we just have $i$ in the solution.
 
-#math #polynomials
+#math #polynomials #complexNumbers