Real Cut 2D
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Notice that the graph of f(z) is symmetric with respect to the real axis. Thus, the branch cut is reflected in the graph as well. This is the reason we can't multiply by i in the first place. We are referring to different parts of the graph of f.
Now consider the following example. The function f(z) = z3 - 2.5 z is shown in the top panel of figure 15.2. The value of f(z) is the graph of the blue curve in the bottom panel. The z values corresponding to a particular value of f(z) are given by the black curve in the bottom panel. The black curve intersects the real axis at three points: -1, 1, and 2.
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