Find the continuous branch cut of a complex logarythm

[hachiroku]

Homework Statement

Find the continuous branch cut of a complex logarythm for C\[iy:y=>0]

One of the complex numbers, for example, is -4i

Homework Equations

I don´t understand what to do with the subset. How could I find the continuous branch cut in the subset?

The Attempt at a Solution

I found the main value: log(2)+i(3pi/2+2kpi)



Thanks

 

[jackmell]

Start with the multi-valued definition of the complex logarithm:

$$\log(z)=\ln|z|+i\arg(z)$$

What's that look like? I mean a picture of the real and imaginary parts of that function. You do Mathematica?