True or false logarithmic branchesSay whether the following are true or false. Give a short...

comAttitRize8

comAttitRize8

Answered

2022-07-20

True or false logarithmic branches
Say whether the following are true or false. Give a short proof.
1) l o g ( z ) + i π is a branch of the logarithmic function whose branch cut is the non-negative real axis
2)If g ( z ) is a branch of the logarithmic function with domain D and h ( z ) is a branch analytic in D, then there is an integer m with h ( z ) = g ( z ) + 2 m π i
Thanks

Answer & Explanation

autarhie6i

autarhie6i

Expert

2022-07-21Added 18 answers

Hint for part a: if z = 1, what happens?
Hint for part b: if g and h share the same domain, what do you know about the branch cuts in relation to each other? How does this relate to the integer multiples of 2 π i?

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