How to use Rouches Theorem to find the zeros in Complex Analysis

This tutorial explains how to use Rouches Theorem to calculate the number of zeros inside an open anulus .
First we test the conditions is the open anulus from 1 to 3 which is a simply connected region on the complex plane and a simple closed contour for which the function is continuous and analytic.
Then we use |z|=3 and find the dominant term in the function , then find the value of the function at the maximum point minus the dominant term .
Then we use |z|=1 and find the dominant term in the function , then find the value of the function at the maximum point minus the dominant term .
Then using the Fundamental Theorem of Algebra we can subtract the 2 totals to give us our answer
#complex
#maths
#euler
#cartesian
#cos
#sin
#exp
#exponential
#math
#formula
#calc3
#calc2