Răspuns:
-1
Explicație pas cu pas:
[tex]\left(\cos\dfrac{\pi}{3} - i\cdot\sin\dfrac{\pi}{3}\right)^{15} = \left(\cos\dfrac{\pi}{3} + i\cdot\sin\left(-\dfrac{\pi}{3}\right)\right)^{15}\stackrel{Moivre}{=}\\ \\ = \cos\dfrac{15\pi}{3} + i\cdot \sin\left(-\dfrac{15\pi}{3}\right) = \cos (5\pi) + i\cdot\sin(-5\pi)= - 1 +i\cdot 0 = -1\\\texttt{Deci partea reala este }\boxed{-1}.[/tex]
