# Infinite sums are not the only heroes!

$\large \displaystyle \sum_{n=1}^{10} {i^{\frac{1}{n}}} = a + bi$

In the equation above, $$a$$ and $$b$$ are positive real numbers. Find the value of $$\left\lfloor a \right\rfloor - \left\lceil b \right\rceil$$.

Notations:

×