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MAT1511 Assignment 1 (ANSWERS) Semester 1 - 2023. Questions asked: 1. Use Descartes’ Rule of Signs to determine the possible number of positive, negative and imaginary zeros of P (x). (i) P (x) = x 4 +x 3 +x 2 +x +12. (4) (ii) P (x) = 2x 5 +x 4 +x 3 −4x 2 −x −3. (4) 2. Let P (x) = x 6 −2x 5 −x 4 +x 3 +2x 2 +x −2 (a) Determine whether (x −2) is a factor of P (x). (2) (b) Find all the possible rational zeros of P (x) by using the Rational Zeros Theorem. (2) (...

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MAT1511 Assignment 2 (Answers) Semester 1 - 2023 Questions asked: 1. Write (2+3i) (4−3i) (3+2i) 2 (4) in the form a+bi, where a,b ∈ R. 2. Given z1 = 2∠180o , ; z2 = 3∠270o and z3 = 1∠180o . Determine the following and leave your answers in rectangular form: (i) (z1) 2 +z2 z2 +z3 (5) (ii) z1 z2z3 (5) 3. Let Z = −1− √ 3i (i) Write Z in a polar form (2) (ii) Use De Moivre’s Theorem to determine Z 4 . (3) Z and leave your answer in polar form with ...

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