Consider the following conditions on a pair of complex numbers z and w: A zw 0,...

 

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Consider the following conditions on a pair of complex numbers z and w: A zw≥ 0, i.e., there is some a 20 for which zu = a. B One of the following three conditions holds: (i) z = 0. (ii) w = 0. (iii) There is some a > 0 for which z = aw. C One of the following three conditions holds: (i) z = 0. (ii) w = 0. (iii) There is some b> 0 for which w = bz. Show conditions A, B, and C are equivalent. (10 presentation points) Consider the following conditions on a pair of complex numbers z and w: A zw≥ 0, i.e., there is some a 20 for which zu = a. B One of the following three conditions holds: (i) z = 0. (ii) w = 0. (iii) There is some a > 0 for which z = aw. C One of the following three conditions holds: (i) z = 0. (ii) w = 0. (iii) There is some b> 0 for which w = bz. Show conditions A, B, and C are equivalent. (10 presentation points)

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ANSWER To show the equivalence of conditions A B and C we will prove a chain of implications in both ... View the full answer