Question: H2.2) (15 pts = 5 + 5 + 5): Suppose that n E N and z is a complex number. (a) If z) = 1

H2.2) (15 pts = 5 + 5 + 5): Suppose that

H2.2) (15 pts = 5 + 5 + 5): Suppose that n E N and z is a complex number. (a) If z) = 1 and 22 -1 then show that is a real number. Use complex exponentials. (b) Consider the equation 23 - (ati)z + B+ 5i =0, (1) where a and 8 are two real numbers. Let ( and ( be the two roots of equation (1). Prove that for any a and B Site=ati. (c) Consider again ( and (2, the two roots of equation (1). For which values of 3 is the the modulus of the product of these roots equal to 13

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