>>13
Log[1+i] = log(2)/2 + i(π/4) = -θ + i(π/4),
[1+i]^[1-i] = (1+i)*(1+i)^{-i}
  = (1+i)*e^{π/4 +iθ},

e^{π/4} = 2.19328
θ =−log(2)/2 = −0.3465736