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Mathematik-Online problems:

Problem 8: Subsets of the Complex Numbers, Complex-Valued Function


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Let be $ w, u \in \mathbb{C}$, $ a, b, c \in \mathbb{R}$ and $ a \neq 0$.
a)
Describe the following subsets of $ \mathbb{C}$:

i) $ M_1 = \{z\in \mathbb{C} \mid az\bar{z} + z\bar{w} + \bar{z}w+b
= 0\}$
ii) $ M_2 = \{z\in \mathbb{C} \mid z\bar{u} + \bar{z}u+c = 0\}$

b)
Show that the map

$\displaystyle f: \, \mathbb{C}\setminus\{0\} \longrightarrow \mathbb{C}\setminus\{0\}, \qquad
z \longmapsto \frac{1}{z}
$

maps lines and circles onto lines and circles, if necessary without origin.

(Authors: Kimmerle/Roggenkamp/Höfert)

see also:


[Solutions]

  automatisch erstellt am 15. 10. 2004