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- Homework Statement
- The function ln (principal value of ln) is known to be analytical in complex plane with removed negative real axis. What is the largest region in which f(z)=ln(iz)-i pi/2 is analytical? Evaluate f′(z).

- Relevant Equations
- Principal value of the logarithm: ln(z) = ln(r) + iArg(z)

Chain rule for complex functions

Inverse functions differentiation rule

Hey everyone! I got stuck with one of my homework questions. I don't 100% understand the question, let alone how I should get started with the problem.

The picture shows the whole problem, but I think I managed doing the a and b parts, just got stuck with c. How do I find the largest region in which f(z) is analytical and how do I get started trying to differentiate it? Do the differentiation rules for the real ln translate to the complex one?

Thanks in advance <3

The picture shows the whole problem, but I think I managed doing the a and b parts, just got stuck with c. How do I find the largest region in which f(z) is analytical and how do I get started trying to differentiate it? Do the differentiation rules for the real ln translate to the complex one?

Thanks in advance <3