If z=reiθz = re^{i\theta}z=reiθ, what is ln(z)\ln(z)ln(z) in the principal branch?
ln(r)+iθ\ln(r) + i\thetaln(r)+iθ
ln(r)\ln(r)ln(r)
r+iθr + i\thetar+iθ
eln(r)+iθe^{\ln(r) + i\theta}eln(r)+iθ