Logarithm rule for branch cut logarithms I know that for a, b in RR , the rule log(ab)=log(a)+log(b) holds.

Siemensueqw

Siemensueqw

Answered question

2022-11-19

Logarithm rule for branch cut logarithms
I know that for a , b R , the rule log ( a b ) = log ( a ) + log ( b )
What about for a 1 , b 1 in the right half-plane, or a 2 , b 2 in the sector from 3 π 4 to 3 π 4 ? For the logarithm, take a branch cut on the negative real line.

Answer & Explanation

Aedan Hatfield

Aedan Hatfield

Beginner2022-11-20Added 16 answers

The logarithm function is f ( x ) = log ( x ) is defined in f : C R C
So, let z 1 = e ρ 1 + i θ 1 , z 2 = e ρ 2 + i θ 2 C , if θ 1 + θ 2 π, then
log ( z 1 z 2 ) = log ( z 1 ) + log ( z 2 ), if θ 1 + θ 2 π, then
log ( z 1 z 2 ) = log ( z 1 ) + log ( z 2 )

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