Question about Logarithmic function

[nickolas2730]

In my complex analysis textbook, there is a definition about log function, which is:
log z := Log |z| + i arg z
= Log |z| + i Arg z + 2kπ where k = 0,±1,±2...

my question is , is there any different between log and Log, and arg and Arg?
If yes, what's the different between them

 

[I like Serena]

Hi nickolas2730!

The difference is that log and arg are so called "multi valued functions".
This means log z is a set of values instead of just 1 value.

Log and Arg are regular functions that yield the so called "principle value".
That is, an argument between 0 and 2pi.

 

[nickolas2730]

oh i see, which means the ans for log and arg must comtain something like 2kπ, which makes them as a set of solution?

 

[I like Serena]

Yep!

 

[nickolas2730]

thank you again =]