Branch values of a complex power ($w^z=\{\exp [z(\mathrm{Log}w+2\pi ik)]:k\in \mathbb{Z}\}$)

For $w\ne 0$, different complex logarithm values differ by $2\pi ik$. Applying the exponential function gives the displayed multivalued power. Selecting a single logarithm branch gives one value. When $z=i$, successive branch values differ by the positive factor $e^{-2\pi }$ and lie on one ray of fixed argument $\ln |w|$. If this factor is not one, the nonzero values accumulate at zero in one direction of the integer index.