1.Consider the complex polynomialp(z) =z^3zin a complex variablez. Solve for allzsuch thatp(z) = 0.

2.Previously it was shown that solvingp(z) =cforcreal has only one real solution for some values ofc. Consider such a value ofc. Prove that if there is a second solution of the formz=a+bi(which requiresb0) then there is a third solution also.

3.Letp(z)andq(z)be polynomials of degree at most 4. Show that ifp(z) =q(z)for5distinct values ofz, thenpandqare equal everywhere in the complex plane.

4.What is a careful statement of the generalization of the previous problem(3) to consider polynomials of degree at mostnfor some positive integern.