# Are these Real numbers? $e^{i}$, $i^{i}$, $\sqrt{i}$

Algebra Level 3

Fill in the Blank:

Some of the following 3 expressions are multi-valued, while the rest has/have only one value: $e^{i},\quad i^{i},\quad \sqrt{i}.$ Also, precisely $\text{\_\_\_\_\_\_}$ of them has/have a value that is strictly real.


Notations:

• $e \approx 2.718$ denotes the Euler's number.
• $i = \sqrt{-1}$ denotes the imaginary unit.
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