Find-the-value-of-log-2-imaginary-

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

Find the value of \log (- 2) {imaginary}

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

you are welcome .

Commented by Dwaipayan Shikari last updated on 26/Jun/20

\log (- 2) = \log (- 1) + \log (2)

= \log (e^{i π}) + \log (2)

= \log (e^{i (2 k π + π)}) + \log (2)

= i π (2 k + 1) + \log (2) {k \in Z}

Is this a solution ? ? ? ? ? ? ?

I am not sure

Commented by mr W last updated on 26/Jun/20

i t h i n k {i t}^{'} s c o r r e c t .

Commented by abdomsup last updated on 26/Jun/20

l n (- 2) = l n (- 1) + l n (2)

l n (e^{i (π + 2 k π)}) + l n (2)

= l n 2 + i (2 k + 1) π (k \in Z)

Commented by Dwaipayan Shikari last updated on 26/Jun/20

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