prove the problem and explain why c is in (0,1)

5. Consider the polynomial P(z) = do + alz + azz2 + . . . + anz" of degree n, where do, a1, . .., an are complex valued constants with an * 0. Show that for any real number c with 0 0 such that P(z)| (1 - c)|an Rn' whenever |z| > R. Note that we used this in the proof of the Fundamental Theorem of Algebra in class. Hint: first show that ao + alz + . . . + an-12"-| R as long as R is sufficiently large. Then show that |P(z) | 2 lanz"|- do + alz + . . . + an-1272 -11