
Complex Analysis Complex Analysis Math Forum 
 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=(x1) does this help me, bit confused with the mod z when applying the integral. ii) similar follows Many thanks 
December 4th, 2016, 04:39 PM  #2 
Senior Member 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. 

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 