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Please help me how to solve this problem. I have no idea how to initiate the solution.

user10354138
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Mathforjob
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1 Answers1

2

$\gamma_1: z = t\\ \gamma_2: z = a + ti\\ \gamma_3: z = a - t + (a-t)i$

Take the derivatives to find $dz$ for each contour

$\int_0^a t \ dt + \int_0^a a (i \ dt) + \int_0^a (a-t)(-1-i\ dt)$

user317176
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  • By your hint , I got 2nd option. But what is a rule by which you constructed the functions? – Mathforjob Jun 18 '19 at 08:08
  • You need a parametric equation for a line that gets you from point to point. If you want to get from $x_0 + iy_0 $ to $x_1+iy_1$ then $z = (x_1-x_0) t + x_0 + ((y_1 - y_0)t + y_0)i$ will get you between those two points. – user317176 Jun 18 '19 at 18:40
  • Is this a general rule for finding parametric equation from one point to another point? I read the result: Let A and B be two extreme points of a curve then Z(t)= A(1-t)+Bt if 0<t<1 . But in above problem, there is no such condition on it. – Mathforjob Jun 19 '19 at 07:45