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incorrect calculation of Log[Exp[...]]

Posted 11 years ago
Log[Exp[(5*I*\[Pi])/3]] - (I*5 \[Pi])/3]
It get the answer -2?i. However, it must be zero. And it also cause the incorrect answer for Residue
Residue[Log[z]/(1 + z^3), {z, E^((I*5 \[Pi])/3)}]
How do I modify my input?
POSTED BY: ChiaWei Tu
"Log[Exp]" does not always equal "a" even though Log and Exp are supposed to be inverse functions. This is because of complex branch cuts. In fact, "Log[Exp]"  can be off  from "a" by a constant factor, in this case a multiple of "2 Pi I".
POSTED BY: Sean Clarke
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