From 2105c12088beae40a680104d181faa958889b574 Mon Sep 17 00:00:00 2001 From: luccul Date: Thu, 1 Jul 2010 14:48:08 +0000 Subject: added problem --- Problem Set 1.page | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) (limited to 'Problem Set 1.page') diff --git a/Problem Set 1.page b/Problem Set 1.page index 91a2a40..60831d3 100644 --- a/Problem Set 1.page +++ b/Problem Set 1.page @@ -10,7 +10,9 @@ You might want to use this fact in the problems below, though it's not necessary. -5. Show that the function $f(z) = \overline{z}$ is not holomorphic, despite being angle-preserving. How does this function transform the complex plane? +- Write down the Cauchy-Riemann equations in polar coordinates. + +6. Show that the function $f(z) = \overline{z}$ is not holomorphic, despite being angle-preserving. How does this function transform the complex plane? - Show that the function $f(z) = z^n$ is holomorphic for any integer n (possibly negative!). How do these functions transform the complex plane? -- cgit v1.2.3