I am reading through the following proof of the Fundamental Theorem of Algebra Simple proofs: The fundamental theorem of algebra and I am not understanding this particular statement...
similarly translate the circle described above. Presumably the polynomial q ( z ) , defined on some circle centered at the origin (which circle is contained within the circle above),
I don't understand the last part in the parenthesis where the author states 'which circle is contained within the circle above'. This implies that the new translated circle is smaller than the original bounding circle defined by B for p(z) since it is translated and still contained within this circle. The original boundary B was defined to establish dominance of the $z^n$ term for p(z); doesn't this new bound, which is less than B , invalidate the dominance of the $z^n$ term?