3. Let D be the annulus $1 < |z| < 5$, and let ? be the circle $|z - 3| = 1$ traversed once in the positive direction starting from the point $z = 4$. Decide which of the following contours are continuously deformable to ? in D. (a) the circle $|z - 3| = 1$ traversed once in the positive direction starting from the point $z = 2$ (b) the point $z = 3i$ (c) the circle $|z| = 2$ traversed once in the positive direction starting from the point $z = 2$ (d) the circle $|z + 3| = 1$ traversed once in the positive direction starting from the point $z = -2$ (e) the circle $|z - 3| = 1$ traversed twice in the negative direction starting from the point $z = 4$
Added by Colin A.
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Step 1: To determine if the given contours are continuously deformable to the contour I in D, we need to check if they have the same starting and ending points, and if they can be continuously deformed without intersecting or crossing any other points. Show more…
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