- #1
Gauss M.D.
- 153
- 1
Homework Statement
Find the number of zeroes of
p(z) = z^5 + 10z - 1
inside |z| < 1
Homework Equations
The Attempt at a Solution
Let f(z) = z^5
g(z) = 10z-1
On |z| = 1:
10|z| - 1< |10z-1| < 10|z| + 1 (is this true...?)
9 < |g(z)| < 11
|f(z)| = 1
So |g| > |f|, so f+g should have the same number of zeroes as f, which is five.
That's incorrect obviously. What am I doing wrong?