We use the logarithmic identity: \[ \log(a) + \log(b) = \log(ab). \] Thus, the expression \( \log(1 + i) + \log(1 - i) \) becomes: \[ \log[(1 + i)(1 - i)] = \log[1^2 - i^2] = \log[1 + 1] = \log 2. \] So, the general value is \( \log 2 \), with the imaginary component arising from the argument of the product of \( (1 + i) \) and \( (1 - i) \), which adds an imaginary factor of \( 4\pi i \).