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Let A = i+212 + 313 + 4i' and B = (1+i)6. (a) Calculate A and B, giving your answer in algebraic form a +

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Let A = i+212 + 313 + 4i' and B = (1+i)6. (a) Calculate A and B, giving your answer in algebraic form a + zy where r and y are real numbers. (6 MARKS) (b) Find rational numbers m and n such that mA* + nB = 1. (4 MARKS) (c) Can we find an integer k such that A = B*? Explain your answer. (4 MARKS)

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