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  3. 5 recall that the set of all polynomials with complex...

Question: 5 recall that the set of all polynomials with complex...

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(5) Recall that the set of all polynomials with complex coefficients is denoted by C[z] (a) Does Cle] have additive inverses? That is, for every polynomial p(z) -an2+...ajz +ao, is there a polynomial q(z) such that p(z)+9()0? If so, state the inverse. If not, give a counter example. (b) Does C[2] have multiplicative inverses? That is, for every nonzero polynomial p(z), is there a polynomial q(z) such that p(z) 9z) 1? If so, state the inverse. If not, give a counter example. c) Is C a field under the operations of polynomial addition and multiplication? Explain your answer. Note: I am not looking for a formal proof, just a short convincing argument)

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