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How to show(Prove) the composition of two polynomials is a polynomial,
the composition of two rational function is a rational function?

We just start learning complex analysis, and there is a formula of complex polynomial function we are given in lecture.

p(z) = $c\prod^{d}_{i=1}(z-a_i)^{m_i}$

where $a_j$ are all distinct, and $m_i$ add to degree p.

Thank you for helps, first time ask a question on MathStack.

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    $\begingroup$ Polynomials are closed under addition. Polynomials are closed under multiplication. Therefore, polynomials are closed under composition. $\endgroup$ – Blitzkrieg Aug 2 '17 at 10:30

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