Complex Number Arithmetic

$i^6 + i^{16} + i^{-26} = i^4\cdot i^2 + (i^4)^4 + \frac{1}{(i^4)^6\cdot i^2} = i^2 + 1 + \frac{1}{i^2} = -1 + 1 + \frac{1}{-1} = \boxed{-1}$