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Mathematik-Online problems:

Problem 7: Sketching of Subsets of the Complex Numbers

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
Find the following subsets of $ \mathbb{C}$ and make a sketch of them in the Gauß plane:

a) $ \{z\in\mathbb{C}\mid \vert z-{\mathrm{i}}\vert < 2\}$       b) $ \{z\in\mathbb{C}\mid {\mathrm{Re}}\,(z) \cdot {\mathrm{Im}}\,(z) \geq 1\}$
c) $ \{z\in\mathbb{C}\mid z+\bar{z} -2 \leq -{\mathrm{i}}(z-\bar{z}) \leq z+\bar{z}+2\}$       d) $ \{z\in\mathbb{C}\setminus\{0\}\mid {\mathrm{Re}}\,(\frac{1}{z}) \geq 1\}$
e) $ \{z\in\mathbb{C}\mid \vert z\vert \leq \arg\,(z)\}$       f) $ \{z\in\mathbb{C}\mid \vert z\vert < \vert z+3\vert\}$
g) $ \{z\in\mathbb{C}\mid 1 < \vert z-{\mathrm{i}}\vert < 2 \, \wedge \, \vert\arg(z) -\frac{\pi}{2}\vert\leq \frac{\pi}{4} \}$   

(Authors: Kimmerle/Roggenkamp/Höfert)

Solution:

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  automatisch erstellt am 29. 10. 2004