Infinite tetration and superroot of infinitesimal

[jaydfox]

(1-i)^i=e

ln(1-i)=1/i=-i is this true?

The absolute value of (1-i) is sqrt(2), and the angle from the origin is -pi/4, so the natural logarithm is ln(sqrt(2))-pi*I/4, or 0.5*ln(2)-(pi/4)*I if you prefer it that way.