I have the following statements written down in my notes. But I can't see what is happening to get from the second last line to the last line.
$e^{\operatorname{Log}(z)} = e^{\log(|z|) + i\operatorname{Arg}(z)} = e^{\log(|z|)}[\cos(\operatorname{Arg}(z)) + i\sin(\operatorname{Arg}(z)] = z$
Anyone know how the second last line is able to reduce into just $z$ on the final line?