# Can the logarithm of a number be negative? Can it be imaginary?

##### 1 Answer

Oct 31, 2015

#### Answer:

Yes and yes, but it gets complicated...

#### Explanation:

If

For example,

#e^z:{a+ib in CC : -pi < b <= pi} -> CC \\ {0}# is a one one function.

If we use this definition then

#ln z:CC \\ {0} -> {a+ib in CC : -pi < b <= pi}#

is well defined and we find values like