Let P(z)= anz + ...+ aiz+ao be a polynomial of degree n (i.e. an # 0)...

 

Transcribed Image Text:

Let P(z)= anz" + ...+ aiz+ao be a polynomial of degree n (i.e. an # 0) and let Q(z) = bmzm ++ b₁z + bo be a polynomial of degree m (i.e. bm #0), where m2n+2. Let C be any positively-oriented simple closed curve enclosing all of the zeros of Q. P(z) Show that dz= 0. (Hint: compute the residue at infinity). Let P(z)= anz" + ...+ aiz+ao be a polynomial of degree n (i.e. an # 0) and let Q(z) = bmzm ++ b₁z + bo be a polynomial of degree m (i.e. bm #0), where m2n+2. Let C be any positively-oriented simple closed curve enclosing all of the zeros of Q. P(z) Show that dz= 0. (Hint: compute the residue at infinity).

Answer rating: 100% (QA)

If f is dinite number of is analytic function except is closed points then Co fcz az Now in ... View the full answer