Complex Logarithm
For with , is defined by , so .
Definition 1.7 (Complex Logarithm)
We define, for and ,
such that
Principal value
Distinct values of differ by integer multiples of . Restricting the argument to selects exactly one of them, mirroring the principal value of the argument.
Example
Since , the arguments of are , so
The logarithm of therefore takes infinitely many values.
Related
Stated in
- Definition 1.7 (Complex Logarithm)§1.7.1 Logarithm