Page 90 - Calculus with Complex Numbers
P. 90
F u n d a m e nt a I t h e o re m of a Ig e b r a 8 I
2. Prove that exactly two zeros of the polynomial .:3 + 9z2 + 9 . z + 9 lie inside
the circle Iz I= 2.
3. Prove that none of the zeros of the polynomial .:3 + 9z2 + 9 .z + 9 lie inside
the circle Iz I= 1/2.
4. Prove that all the zeros of the polynomial .:3 + 6 .: + 8 lie between the two
circles I z I= 1, Iz I = 3.
5. Prove that the polynomial ./ + c + 1 has one zero in each quadrant.
