28. Complex Numbers question bank (Maths)

Let \(i^2 = -1\). Then \(\left(i^{10} - \frac{1}{i^{11}}\right) + \left(i^{11} - \frac{1}{i^{12}}\right) + \left(i^{12} - \frac{1}{i^{13}}\right) + \left(i^{13} - \frac{1}{i^{14}}\right) + \left(i^{14} + \frac{1}{i^{15}}\right) =\)  

The value of \(\sum_{n=1}^{13}(i^n+i^{n+1})\) where \(i=\sqrt{-1}\) equals