My Math Forum  

Go Back   My Math Forum > College Math Forum > Complex Analysis

Complex Analysis Complex Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 4th, 2016, 04:09 PM   #1
Newbie
 
Joined: Dec 2016
From: England

Posts: 4
Thanks: 0

Complex Integration

I am very stuck on this!

i ) i worked out the straight line is y=(x-1) does this help me, bit confused with the mod z when applying the integral.

ii) similar follows

Many thanks
Attached Images
File Type: jpg Screen Shot 2016-12-05 at 00.06.41.jpg (19.3 KB, 2 views)
ryancooperx is offline  
 
December 4th, 2016, 04:39 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 760
Thanks: 400

the first parameterization is

$z = 1 + (1+i)t,~0\leq t \leq 1$

$z = (1+t)+it$

$|z|^2 = (1+t)^2 + t^2 = 2t^2 + 2t + 1$

$\displaystyle{\int_0^1}~2t^2 + 2t + 1 = \left. \dfrac{2 t^3}{3}+t^2+t\right|_0^1 =\dfrac 8 3$

for the 2nd parameterization

$z = (1+t) + t^2 i,~0\leq t \leq 1$

See if you can figure out the form of $|z|^2$ and do the integration.

Note this also goes from $1 \to (2+i)$ but by a different path.
romsek is offline  
Reply

  My Math Forum > College Math Forum > Complex Analysis

Tags
complex, integration, plane, smooth



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Complex Integration WWRtelescoping Complex Analysis 1 May 7th, 2014 05:52 AM
Complex integration. yotastrejos Complex Analysis 1 August 18th, 2013 08:24 AM
Complex integration of cos^2 z, please help? szak1592 Complex Analysis 1 April 2nd, 2013 01:15 PM
Complex integration using CIF Grayham1990 Complex Analysis 14 November 3rd, 2011 04:37 AM
Complex Integration xboxlive89128 Complex Analysis 0 October 1st, 2009 10:46 PM





Copyright © 2017 My Math Forum. All rights reserved.