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5. [8 marks] Consider the quartic equation z* + 42 + 82 + 80z + 400 = 0, Z E C. Two of the roots

5. [8 marks] Consider the quartic equation z* + 42 + 82 + 80z + 400 = 0, Z E C. Two of the roots of this equation are a + bi and b + ai, where a, be Z. Find the possible values of a

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