Consider the line segment parametrized by z(t) = z0 + reit , 0 ≤ t ≤ 2π.
(a) Find a parametrization of the image of the line segment under the translation T (z) = z + b, b ≠ 0. Describe the image in words.
(b) Find a parametrization of the image of the line segment under the rotation R(z) = az, |a| = 1. Describe the image in words.
(c) Find a parametrization of the image of the line segment under the magnification M(z) = az, a > 0. Describe the image in words.
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