czesc, prosze o sprawdzenie zadania.
\(\displaystyle{ (\frac{1-i \sqrt{3} }{2}) ^{15}}\)
\(\displaystyle{ z= \frac{1-i \sqrt{3} }{2}= \frac{1}{2} - \frac{i \sqrt{3} }{2}}\)
\(\displaystyle{ \left| z\right| = \sqrt{ (\frac{1}{2} ) ^{2} - (\frac{i \sqrt{3} }{2}) ^{2} } = \sqrt{ \frac{1}{4} - \frac{i ^{2}*3 }{4} } = \sqrt{ \frac{1}{4} + \frac{3}{4} } = 1}\)
\(\displaystyle{ cosSIGMA= \frac{1}{2} sinSIGMA= \frac{ \sqrt{3} }{2}}\)
\(\displaystyle{ SIGMA = \frac{Pi}{3}}\)
\(\displaystyle{ z=1(cos \frac{pi}{3} + isin \frac{pi}{3} )}\)
\(\displaystyle{ z ^{15}= 1(cos \frac{15pi}{3} +isin \frac{15pi}{3} ) = 1}\)
dzieki. pozdro
