From 93b6675157aed7f03bf0befc4fcc0fdd7fb657b2 Mon Sep 17 00:00:00 2001 From: luccul Date: Thu, 1 Jul 2010 01:06:07 +0000 Subject: Fixed probs 7-9 to a bit make more sense --- Problem Set 1.page | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) (limited to 'Problem Set 1.page') diff --git a/Problem Set 1.page b/Problem Set 1.page index 91d2a30..91a2a40 100644 --- a/Problem Set 1.page +++ b/Problem Set 1.page @@ -14,9 +14,11 @@ - Show that the function $f(z) = z^n$ is holomorphic for any integer n (possibly negative!). How do these functions transform the complex plane? -- Show that the sum of two holomorphic functions is holomorphic; conclude that any polynomial function is holomorphic. +- Show that the sum of two holomorphic functions is holomorphic. -- Show that the product of two holomorphic functions is holomorphic. +- Show that the product of two holomorphic functions is holomorphic + +- Conclude that any polynomial function is holomorphic. - Try to extend the following functions of a real variable to holomorphic functions defined on the entire complex plane. Is it always possible to do so? What goes wrong? a. $\sinh(z), \cosh(z)$ -- cgit v1.2.3