How to derive the value of log(−1)? My book gives the following relation which I cannot derive myself. How to approach it? log(−1)=(2n+1)pi i,n=0,+-1,... The definition of logarithm I am using is, logz is any complex number w such that e^w=z.

vedentst9i

vedentst9i

Answered question

2022-11-11

How to derive the value of log ( 1 )?
My book gives the following relation which I cannot derive myself. How to approach it?
log ( 1 ) = ( 2 n + 1 ) π i , n = 0 , ± 1 , . . .
The definition of logarithm I am using is, log z is any complex number w such that e w = z

Answer & Explanation

Haylie Park

Haylie Park

Beginner2022-11-12Added 14 answers

Hint
Using Euler identity, for integer n,
cos ( ( 2 n + 1 ) π ) + i sin ( ( 2 n + 1 ) π ) = e i ( 2 n + 1 ) π = 1

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