IMO Shortlist 1969 problem 6
Dodao/la:
arhiva2. travnja 2012. ![(BEL 6)](/media/m/7/7/3/77319c2a1e9e7ed979f06d7774203927.png)
Evaluate
![\left(\cos\frac{\pi}{4} + i \sin\frac{\pi}{4}\right)^{10}](/media/m/2/4/b/24b17f31fae47f10f2c92c93075384ea.png)
in two different ways and prove that
%V0
$(BEL 6)$ Evaluate $\left(\cos\frac{\pi}{4} + i \sin\frac{\pi}{4}\right)^{10}$ in two different ways and prove that $\dbinom{10}{1}-\dbinom{10}{3}+\frac{1}{2}\dbinom{10}{5}=2^4$
Izvor: Međunarodna matematička olimpijada, shortlist 1969