My Math Forum Complex Integration

 Complex Analysis Complex Analysis Math Forum

December 4th, 2016, 04:09 PM   #1
Newbie

Joined: Dec 2016
From: England

Posts: 7
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
 Screen Shot 2016-12-05 at 00.06.41.jpg (19.3 KB, 2 views)

 December 4th, 2016, 04:39 PM #2 Senior Member     Joined: Sep 2015 From: Southern California, USA Posts: 1,607 Thanks: 819 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 Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post WWRtelescoping Complex Analysis 1 May 7th, 2014 06:52 AM yotastrejos Complex Analysis 1 August 18th, 2013 09:24 AM szak1592 Complex Analysis 1 April 2nd, 2013 02:15 PM Grayham1990 Complex Analysis 14 November 3rd, 2011 05:37 AM xboxlive89128 Complex Analysis 0 October 1st, 2009 11:46 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top