Determine if the contours within I can be deformed to the indicated contour. Jus

Question

Determine if the contours within I can be deformed to the indicated contour. Justify your answer. (a) The circle l-31- 1 traversed once in the positive direction into the circle +3i2 traversed twice in the negative direction. (b) The dashed line contour into (c) The circle 1-3-1 traversed once in the positive direction into the circle Irl = 3 traversed once in the positive direction. (d) The circle la]-400 traversed once in the positive direction into r. (e) The circle -1 traversed once in the positive direction into 40

Explanation / Answer

In this question we only have to check whether the transformed contour satisfies all the conditions of given contour including the direction of contour. Now coming to part (a) we will check that the circle the given circle is of radius 1 and center of this circle lies on (3,0) also it has been transversed once in the positive direction into a circle of radius 2 and center at (0,3) which is again twice transversed into negative direction. So all this transformation lies within given contour.

Other parts can also be done like this.

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