• Support PF! Buy your school textbooks, materials and every day products Here!

Analysis/Complex Analysis

  • Thread starter oab729
  • Start date
  • #1
12
0

Homework Statement


Show that for a polynomial of degree n, P(z), that for all z with |z| sufficiently large, there are positive constants c,d, s.t. c|z|^n < |P(z)| < d|z|^n


Homework Equations





The Attempt at a Solution


Assume it is true for n-1.
p(z)=az^n+q(z)
Then for z with sufficiently large |z|, there exist e,f s.t. e|z|^(n-1) < |q(z)| < f|z|^(n-1).

No idea how to continue.
 

Answers and Replies

  • #2
392
0
Try doing |P(z)| < d|z|^n and c|z|^n < |P(z)| as two different problems. Use triangle inequality. Try it with actual example polynomials first if you're still lost.
 

Related Threads for: Analysis/Complex Analysis

  • Last Post
Replies
1
Views
498
  • Last Post
Replies
18
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
830
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
909
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
4
Views
995
Top