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| author | luccul <luccul@gmail.com> | 2010-07-01 01:06:07 +0000 |
|---|---|---|
| committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-07-01 01:06:07 +0000 |
| commit | 93b6675157aed7f03bf0befc4fcc0fdd7fb657b2 (patch) | |
| tree | 155f7632704b6b91889af0b54cc07ce220d58ca1 /Problem Set 1.page | |
| parent | 0c0506787f7cfd76ebfa8ec68e109fbc1130b5b4 (diff) | |
| download | afterklein-wiki-93b6675157aed7f03bf0befc4fcc0fdd7fb657b2.tar.gz afterklein-wiki-93b6675157aed7f03bf0befc4fcc0fdd7fb657b2.zip | |
Fixed probs 7-9 to a bit make more sense
Diffstat (limited to 'Problem Set 1.page')
| -rw-r--r-- | Problem Set 1.page | 6 |
1 files changed, 4 insertions, 2 deletions
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. $\sinh(z), \cosh(z)$ |