Which of the following is \((e^i)^2\)?
\(e^2\)
\(e^{-1}\)
\(e^{2i}\)
The answer is \(e^{2i}\).
Note that \(e^i = \operatorname{cis} 1\). By De Moivre'e Formula, we get that \((e^i)^2 = \operatorname{cis} 2 = e^{2i}\).