I have the following homework (Complex Ana):

Let C be the perimeter of the square with
vertices at the points z = 0, z =1, z =1+ i, and
z = i traversed in that order. Show that
Integral of C of (e ^ z) dz = 0;

I worked out the mechanics of it,
z(1) = t 0

Question

I have the following homework (Complex Ana):

Let C be the perimeter of the square with
   vertices at the points z = 0, z =1, z =1+ i, and
   z = i traversed in that order. Show that
   Integral of C  of (e ^ z) dz = 0;

I worked out the mechanics of it,
       z(1) = t    0<= t <=1
       z(2) = 1+ti 
       z(3) = 1 + i - ti
       z(4) = i - ti
      
    Summation of all z(t):  f(z(n)) z'(n) dt = 0; for n = 1,2,3,4

So it is OK mechanically; but I have a hard time
   to visualize (or understand) the relationship
   of (e^z) to perimeter of square. What is it?
   Can anyone help? Thanks a lot.
DL

Updated: I think I know the answer. f(z) is like a transformation function applying to
               z(t); like f(z)=inverse z;

anonymous · Answer

more edits: 
   1) z = 1 + 1; (instead of z 1 +i);
    2) Summation of 4 integrals (f(z(n)) z'(n) dt for n  = 1, 2, 3 ,4 is 0
Sorry

anonymous · Answer

more edit: Integral of C of (e ^ z) dz = 0