Do logarithm to complex number get strange result.

vv=1-80i;
a=exp(vv);
b=log(a);

in my research, I need to do log to some complex number, but it seems that the result are not invertable.

This is really strange, anyone knows what's happened?

Answer 1

[Matt J]

Because for any integer, k,

and so clearly log() cannot uniquely determine what the imaginary part of the original number was.

[Matt J]

Tiexing Wang's comment moved here:

Thank you for your answer, it's really helpful.