MATH1021: Calculus of One Variable Semester 2, 2022
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Assignment 1
MATH1021: Calculus of One Variable
Semester 2, 2022
This assignment is worth 5% of your final assessment for this course. Your answers should be well written, neat, thoughtful, mathematically concise, and a pleasure to read. Please cite any resources used and show all working. Present your arguments clearly using words of explanation and diagrams where relevant. After all, mathematics is about communicating your ideas. This is a worthwhile skill which takes time and effort to master. The marker will give you feedback and allocate an overall mark to your assignment using the following criteria:
1. Let A = {1, 2, 4, 5, 7, 9}, B = {2, 3, 4, 8, 9}, C = {1, 4, 6, 7, 8} and D = {3, 4, 6, 7}. (a) Find A ∩ B .
(b) Find (A/C) n (B/D). ==================================================
2. Express the following complex numbers in Cartesian form z = a + ib.
(a) z = (4 + 3i)(5 − 2i).
(b) z = i87 /(−2 + 3i).
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3. Let w = 3 − 3i and z = −2 + 2^3i.
(a) Express w and z in polar exponential form.
(b) Express (wz)10 in polar exponential form using the principal argument. ==================================================
4. Find all solutions z ∈ C of the following equations. (a) z5 − 32i = 0
(b) z4 − 6z3 + 11z2 − 46z + 170 = 0
(Given that z = 4 − i is one solution.)
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2022-08-25