How do you identify the constant of proportionality when given a graph?
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Not much can be done without knowing what 
is, but at the least we can set up the integral.
First parameterize the pieces of the contour:
where
and 
. You have
and so the work is given by the integral
First parameterize the pieces of the contour:
where
and so the work is given by the integral
47 -14i
You can work this out in the straight-forward way, or you can recognize that (6-i) is a common factor. In the latter case, you have ...
... = (6-i)(5 + 3-i)
... = (6 -i)(8 -i)
This product of binomials is found in the usual way. Each term of one factor is multiplied by each term of the other factor and the results summed. Of course, i = √-1, so i² = -1.
... = 6·8 -6i -8i +i²
... = 48 -14i -1
... =
_____
A suitable graphing calculator will work these complex number problems easily.
