Difference between revisions of "TU Wien:Algebra und Diskrete Mathematik UE (diverse)/Übungen SS19/Beispiel 36"

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(beispiel_fixer.py)
 
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Latest revision as of 17:52, 7 March 2019

Man berechne ohne Taschenrechner alle Werte von \sqrt[4]{1+i} in der Form [r, \phi].

z_1 = 1 + i = [\sqrt{2}, \frac{\pi}{4}]

Nützliches[edit]

\phi = arctan(b/a)

z = [r, \phi]

\sqrt[n]{z}= [\sqrt[n]{r}, \frac{\phi}{n} + \frac{2k\pi}{n}]

Lösung[edit]

w_0 = [\sqrt[8]{2}, \frac{\pi}{16}]

w_1 = [\sqrt[8]{2}, \frac{\pi}{16} + \frac{\pi}{2}]

w_2 = [\sqrt[8]{2}, \frac{\pi}{16} + \pi]

w_3 = [\sqrt[8]{2}, \frac{\pi}{16} + \frac{3\pi}{2}]