# What is $\ln(e^{ix})$?

What is $$\ln(e^{ix})$$? Why isn't it $$ix$$?

• because complex logs have branches. Which branch are you working in? – gt6989b Oct 29 '18 at 20:25
• The complex logarithm is multivalued and so the possible values are $\log(e^{ix})=i (x+2n\pi)$ for integer values of $n$ – Mark Viola Oct 29 '18 at 20:28
• Thank you both. – Malcolm Regan Oct 29 '18 at 20:31