True or false logarithmic branchesSay 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 axis2)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 iThanks

Question

True or false logarithmic branchesSay 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 axis2)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    iThanks

autarhie6i · Accepted Answer

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?