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show that $|z|<1$

Source: Moldova TST 2001

August 7, 2023
complex numbers

Problem Statement

If z∈Cz\in\mathbb{C} is a solution of the equation xn+a1xn−1+a2xn−2+…+an=0x^n+a_1x^{n-1}+a_2x^{n-2}+\ldots+a_n=0 with real coefficients 0<an≤an−1≤…≤a1<10<a_n\leq a_{n-1}\leq\ldots\leq a_1<1, show that ∣z∣<1|z|<1.
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