Every non-zero complex number has precisely four fourth roots, lying at the vertices of a square centered at 0. To get a continuous fourth root function, we may slit the plane by removing the negative real axis. The resulting fourth root that is real and positive along the positive real axis is the "principal branch" of fourth root, whose image is light green. The other three branches, obtained by rotating the image 1/4, 1/2, or 3/4 of a turn about 0, fit neatly together.
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