Hi I have been trying this question for days but cannot get to the answer. This question seems to be a lot tough. I tried many ways but cannot reach the answer. It will be a humble request if anyone solves this. question has been attached as a link above.
I have tried this question by simplifying the root terms , I used $\;\sqrt2+1=\dfrac1{\sqrt2-1}\;.$
But nothing came out i think this is a mixed up of two series .
It's the binomial expansion of $$\left(e^{\frac{i\pi}{2}}\sqrt{\frac{\sqrt{2} - 1}{2\sqrt{2}}} + \sqrt{\frac{\sqrt{2} + 1}{2\sqrt{2}}}\right)^{64}$$
You can simplify this and write it like: $$\left(\frac{e^{\frac{i \pi}{2}} \sqrt{2 - \sqrt{2}}}{2} + \frac{\sqrt{\sqrt{2} + 2}}{2}\right)^{64}$$ Can you take it from here?