Note $a_0$ is not equal to $0$ and $\eta$ is positive and sufficiently small.
Q. I can't seem to grasp how the inequalities were deduced, any help will be appreciated.
Inequality - Complex Valued Polynomial
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complex-analysis
polynomials
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0$$|P(\eta\exp i\theta )|\le |a_0|-|b_m|\eta^m+|a_0|\eta^{m+1}\sum_{j=m}^n|b_j|$$ should be $$|P(\eta\exp i\theta )|\le |a_0|-|a_m|\eta^m+|a_0|\eta^{m+1}\sum_{j=m}^n|b_j|.$$ – 2017-01-22
1 Answers
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Hint: Triangle Inequality, bound using $\eta$ is very small.