Math Problem Solver

$\sqrt{a} + \frac{1}{\sqrt{a}} \in \left\{- i^{\frac{3}{2}} + \sqrt{i}, \sqrt{- i} + \frac{1}{\sqrt{- i}}\right\}$

$i$ is the imaginary unit, defined as $i^2 = -1$.

By substituting this value into the expression, we find that: $$\begin{aligned}\sqrt{a} + \frac{1}{\sqrt{a}} &= \frac{1}{\sqrt{i}} + \sqrt{i}\\&= - i^{\frac{3}{2}} + \sqrt{i}\end{aligned}$$