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Unformatted text preview: complex numbers C . (Hint: Could 0 i ?) 7. Describe geometrically the set of points z in the complex plane dened by the following relations: (a) | z-1 + i | = 1 (b) | z-a | = | z-b | for given complex numbers a, b with a 6 = b . (c) 1 z = z 1 (d) Re ( z ) = 3 (e) Re ( z ) > c where c R (f) Re ( az + b ) > 0 for given complex numbers a, b . (g) | z | = Re ( z ) + 1 (h) Im ( z ) = c with c R 8. (a) Show that every convergent sequence is bounded. Give an exam-ple of a bounded sequence which is NOT convergent. (b) Give an example of a sequence of complex numbers with innitely many distinct accumulation points (c) Show that a convergent sequence has exactly one accumulation point. Give an example of a sequence which is NOT convergent with exactly one accumulation point. 2...
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- Fall '07