a) Show that a set A of complex numbers is bounded if and only if, given...

 

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a) Show that a set A of complex numbers is bounded if and only if, given 20 € C, there exists a positive real number M such that z E D(20; M) for every z E A. b) Prove that each of the following sequences {zn} converge, and give the limits: i) zn = n²+in n2+i ii) zn = Li" c) Investigate the double sequence {zmn}, where zmn n+m with regards to convergence n-im and existence of iterated limits. a) Show that a set A of complex numbers is bounded if and only if, given 20 € C, there exists a positive real number M such that z E D(20; M) for every z E A. b) Prove that each of the following sequences {zn} converge, and give the limits: i) zn = n²+in n2+i ii) zn = Li" c) Investigate the double sequence {zmn}, where zmn n+m with regards to convergence n-im and existence of iterated limits.