The only zeros of the function . ::-' + 2 ) 2 j(:) = - =
Chapter 0, Problem 7.40(choose chapter or problem)
The only zeros of the function . ::-' + 2 ) 2 j(:) = - = ::- +-=- arc exterior lo the circle I: I = I. since they arc the cube roots of -2: and the only singularity in the finite plane is a simple pole at the origin. Hence. if C denotes the circle 1:1 = 1 in lhc positive direction, our theorem tells us lhal ~ c = 2n ( o - 1 > = - 2 n. Thal is. the image r of C under lhc transfonnation u: = f (:.)winds around the origin u1 = 0 once in the clockwise direction.
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