1. The problem statement, all variables and given/known data Given sin x = (eix - e-ix) / 2i, I want to prove that arcsin x = -i ln(ix + √1 - x2) 2. Relevant equations I know about the Euler's formula and complex number. But I have never learnt about complex logarithms. 3. The attempt at a solution I try to use x = sin y. But it seems not working. How to show that relation?