Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

Lösung 3.3:1c

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
K (Solution 3.3:1c moved to Lösung 3.3:1c: Robot: moved page)

Version vom 10:43, 11. Mär. 2009

The calculation follows a fairly set pattern. We write the number 43−4i  in polar form and then use de Moivre's formula.

Image:3_3_1_c.gif Image:3_3_1_c_text.gif

This gives

43−4i=8cos−6+isin−6 

and then we get, on using de Moivre's formula,

43−4i22=822cos22−6+isin22−6=2322cos−311+isin−311=2322cos−312−+isin−312−=266cos−4+3+isin−4+3=266cos3+isin3=26621+i23=265(1+i3).
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.3:1c“