= Solution
A <branch point> obstructs a single-valued <analytic continuation> around a closed circuit. Continuing $\log z=\log|z|+i\theta$ once around zero increases its value by $2\pi i$. A <branch cut> removes a curve joining <Branch point>[branch points] or extending to infinity so that a continuous <argument> can be chosen on the remainder. Zero and infinity are <Logarithmic branch point>[logarithmic branch points]; the positive-axis cut used here selects $0<\arg z<2\pi$. The cut is a choice of representation, not a line of <Pole>[poles] of the multivalued <logarithm>.
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