Question Number 100442 by Dwaipayan Shikari last updated on 26/Jun/20

Find the value of     log(−2)  {imaginary}

Commented bymathmax by abdo last updated on 26/Jun/20

you are welcome.

Commented byDwaipayan Shikari last updated on 26/Jun/20

log(−2)=log(−1)+log(2)                     =log(e^(iπ) )+log(2)                         =log(e^(i(2kπ+π)) )+log(2)                      =iπ(2k+1)+log(2)    {k∈Z}  Is  this a solution???????  I am not sure

Commented bymr W last updated on 26/Jun/20

i think it′s correct.

Commented byabdomsup last updated on 26/Jun/20

ln(−2) =ln(−1)+ln(2)  ln(e^(i(π+2kπ)) )+ln(2)  =ln2 +i(2k+1)π    (k∈Z)

Commented byDwaipayan Shikari last updated on 26/Jun/20

Thanking you for your confirmation Mr.W sir and Abdomsup sir