Editing Argument principle (section)

==Interpretation of the contour integral==
The [[contour integral]] <math>\oint_{C} \frac{f'(z)}{f(z)}\, dz</math> can be interpreted as 2&pi;''i'' times the winding number of the path ''f''(''C'') around the origin, using the substitution ''w'' = ''f''(''z''): 
:<math>\oint_{C} \frac{f'(z)}{f(z)}\, dz = \oint_{f(C)} \frac{1}{w}\, dw</math>
That is, it is ''i'' times the total change in the [[argument (complex analysis)|argument]] of ''f''(''z'') as ''z'' travels around ''C'', explaining the name of the theorem; this follows from 
:<math>\frac{d}{dz}\log(f(z))=\frac{f'(z)}{f(z)}</math> 
and the relation between arguments and logarithms.