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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 deﬁned by the following relations: (a)  z1 + i  = 1 (b)  za  =  zb  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 example of a bounded sequence which is NOT convergent. (b) Give an example of a sequence of complex numbers with inﬁnitely 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
 Lim
 Math, Complex Numbers, Complex number, convergent sequence, nth root, distinct accumulation points

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