Find the continuous branch cut of a complex logarythm

hachiroku

1. 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

2. Homework Equations

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

3. The Attempt at a Solution

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

Thanks

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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?

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