An Illustration of the Argument Principle

r

contour	image

In the complex plane, consider the image of the contour

γ={|z|=r}

under the map

p(z)=

6

z

+6z+10

. The argument principle states that the number of roots of

p(z)

enclosed by

γ

is equal to the winding number of the origin in the image. As you vary

r

you can see how this winding number changes.