Obliczyc wartosc.

[r2b]

Obliczyc:

\(\displaystyle{ (\frac{1+i}{ \sqrt{2} }) ^{26}}\)

Wynik to i.Mi niestety wychodza jakies glupoty tzn sin=cos.

[Lorek]

\(\displaystyle{ (\frac{1+i}{\sqrt{2}})^{26}=(\cos \frac{\pi}{4}+i\sin\frac{\pi}{4})^{26}=\cos \frac{26\pi}{4}+i\sin \frac{26\pi}{4}=\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}=i}\)

[r2b]

[/size]

\(\displaystyle{ \cos \frac{26\pi}{4}+i\sin \frac{26\pi}{4}=\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}=i}\)

Jak Ci to wyszlo?

[Lorek]

\(\displaystyle{ \frac{26\pi}{4}=6\pi+\frac{\pi}{2}}\)
i wzory redukcyjne