Complex function z^z
It is common to encounter the following question: is i to the i real or complex? The proof that is real is reasonably simple, but I became curious to examine the complex function . In this construction, I considered the image set of a circle with radius r (initially set to ).
The red curve represents the image of the black circle. The point is the image of the point . The slider represents the angle of the complex number which belongs to the circle . Note that if then .