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1. (2 marks) Let Z = - 4 + 3i. Evaluate each of the following exactly. Your answers should be as simple as possible and in rectangular form. Show your work. a. Z b. 2 -1 C. 22 d. /z| a + 2i 2. (2 marks) Find all real numbers a such that = 2. Justify your answer. 4 - 2 3. (2 marks) Let P2 denote the set of polynomials in x with real coefficients having degree at most two. Let f : P2 R² be given by f(ax2 + bx + c) = [ b-c a + 2c a. What is f(-4x+3)? b. Give an element p € P2 such that f(p) = [3 . Justify your answer. 4. (2 marks) Simplify 4i 1 + -3 : 3 i 2 - as much as possible. Show your work. -2

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