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The instructions and problems for a group assignment in a university-level mathematics course (math 412) during the spring 2009 semester. The assignment includes introducing yourself to group members, evaluating complex expressions, and sketching points in the complex plane. Problems involve complex numbers, absolute values, and inequalities.
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Problem 0. Introduce yourself to anyone in your group who you don’t know. Problem 1. Evaluate each of the following: (a): (4 − i)(1 − 3 i) −1 + 2i
(b): Im
x − iy
Problem 2. In the complex plane, sketch the points determined by (a): |z + 1 − 2 i| = 2. (b): Im(z − 2 i) > 6. Problem 3. Show that (a): |z 1 − z 2 | ≥ |z 1 | − |z 2 |. (b):
z 1 z 2
z 1 z 2
