This is is because exponentiation to an imaginary power can also be thought of as rotation. You have presumably heard e^(pii) = -1. That's because it's a half-rotation away from 1. Half of that half rotation would be i, and is sqrt(e^(pi i)), which is e^(pi/2*i), which is equivalent to (e^(pi/2))^i, and the ith root of that is obviously (e^(pi/2)).
This is is because exponentiation to an imaginary power can also be thought of as rotation. You have presumably heard e^(pii) = -1. That's because it's a half-rotation away from 1. Half of that half rotation would be i, and is sqrt(e^(pi i)), which is e^(pi/2*i), which is equivalent to (e^(pi/2))^i, and the ith root of that is obviously (e^(pi/2)).