The plots in the z plane on the left hand side and the f(z) plane on the right hand side illustrate one quality of the complex power i of a general complex number, i.e. zi. What points of z map to the real line under f(z) = zi? They include all points on circles of radius e0 π, eπ, e2π, e3π, ... .
Because of the large values of |z|, we plotted circles with radius ln(emπ), which of course is mπ. That is why the first circle, which has radius 1, is plotted as a point at the origin. The points 1, -1, i, -i fall on this inner circle.
In the f(z) domain, points of f(z), m = 1, 2, 3, ... are plotted a little off the real line so they don't overlap and obscure one another. Points of even-numbered circles go to positive reals, and points of odd-numbered circles go to negative reals. The figure is based on Needham's Chapter 2, Exercise 30, p. 119.