Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2006 / Paper 1 / 3 / b / iii / Solution

Complex exponentiation uses a branch of the complex logarithm. All logarithms of $i$ are $i(\pi /2+2\pi k)$ with $k\in \mathbb{Z}$, soSince the trigonometric factor is always $i$, all values in Cartesian form areThe principal logarithm selects $k=0$ and gives the principal value $i{e}^{\pi /2}$.