See also
Argument Principle Explore with Wolfram|Alpha
References
Challener, D. and Rubel, L. "A Converse to Rouché's Theorem." Amer. Math. Monthly 89, 302-305, 1982.Estermann, T. Complex Numbers and Functions. London: Oxford University Press, p. 156, 1962.Knopp, K. Theory of Functions Parts I and II, Two Volumes Bound as One, Part II. New York: Dover, p. 111, 1996.Krantz, S. G. "Rouché's Theorem." §5.3.1 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 74, 1999.Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 22, 1975.Referenced on Wolfram|Alpha
Rouché's Theorem Cite this as:
Weisstein, Eric W. "Rouché's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RouchesTheorem.html
Subject classifications
and 
analytic in 
with 
a simple loop homotopic to a point in 
, if 
for all 
on 
, then 
and 
have the same number of roots inside 
. 