Math 5283, HW Set 1, Fall 2006
Due: Friday, September 1, 2006
1. (D. Ullrich’s book, Appendix A2) Show that the principal-value argument
function
Arg : C\ {0} → (−π, π]
which assings to any non-zero complex number its unique argument in (−π, π]
in not a continous function.
2. Show that Cis not an ordered field.
3. Page 9, Problem 3 and Page 11, Problem 1 in Ahlfors.
4. Page 9, Problem 5 in Ahlfors.
5. Page 17, Problem 5 in Ahlfors.
6. Page 20, Problem 1 in Ahlfors.
7. Show that the -δdefinition of limz→af(z) = Ais equivalent to the sequence
definition.
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