Let d consist of all z in the rectangle having vertices a

Question

Question: Let D consist of all z in the rectangle having vertices ± α i and π ± α i, with α a positive number.

(a) Determine the image of D under the mapping w = cos(z). Sketch D and its image.

(b) Determine the image of D under the mapping w = sin(z). Sketch this image.

(c) Determine the image of D under the mapping w = 2z². Sketch this image.