math185f08-hw3 - MATH 185: COMPLEX ANALYSIS FALL 2008/09...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 185: COMPLEX ANALYSIS FALL 2008/09 PROBLEM SET 3 C will always denote a region unless specified otherwise. For f : C and c C a constant, we write f c to mean that f ( z ) = c for all z . 1. Let f : C with f ( x + iy ) = u ( x,y )+ iv ( x,y ). Let z and suppose there exists a function : C C such that lim h f ( z + h )- f ( z )- ( h ) h = 0 . Recall from Problem Set 2 , Problem 2 that f is real differentiable if is real linear and f is complex differentiable if is complex linear. Recall from Problem Set 2 , Problem 1 that a real linear satisfies ( x + iy ) = ( ax + by ) + i ( cx + dy ) (1.1) for some a b c d R 2 2 and a complex linear satisfies ( x + iy ) = ( ax- cy ) + i ( cx + ay ) (1.2) for some [ a c- c a ] R 2 2 . (a) Show that if f is real differentiable at z = x + iy , then the matrix a b c d is given by a b c d = u x ( x ,y ) u y ( x ,y ) v x ( x ,y ) v y ( x ,y ) ....
View Full Document

Page1 / 2

math185f08-hw3 - MATH 185: COMPLEX ANALYSIS FALL 2008/09...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online