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Mathematik-Online problems:

Problem 5: Real and Imaginary Part of 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 a representation like $ a+{\rm {i}}\,b$ with $ a,b\in\mathbb{R}$ for the following complex numbers:
a)      $ {\displaystyle{z = \frac{2-{\rm {i}}}{1+{\rm {i}}}}}$           b)      $ {\displaystyle{z = \frac{\sqrt{3}+2\sqrt{2}\,{\rm {i}}}{\sqrt{3}-\sqrt{2}\,{\rm {i}}}}}$           c)      $ {\displaystyle{z = \frac{(2+{\rm {i}})(3-2{\rm {i}})(1+2{\rm {i}})}{(1-{\rm {i}})^2}}}$
d)      $ z = (1-2{\rm {i}})^4$           e)      $ z = \sqrt[3]{\,\rm {i}}$           f)      $ {\displaystyle{z = \frac{\left[{\textstyle{2(\cos \frac{\pi}{12}+{\rm {i}}\sin... ...eft[{\textstyle{4(\cos \frac{\pi}{4}+{\rm {i}}\sin \frac{\pi}{4})}}\right]^3}}}$

(Authors: Kimmerle/Roggenkamp/Kirchgaessner/Brenner/Werner/Höfert)

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  automatisch erstellt am 29.  7. 2009