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**slevvio** Show that the only units of $\displaystyle \mathbb{C} [ X]$ are the non-zero complex number, i.e. The non zero complex polynomials.

Hint: suppose p = $\displaystyle \sum_{r=o}^{n} a_r X^r $ is a unit and let $\displaystyle p^{-1} = \sum_{s=o}^{m} b_s X^s $ be its inverse.

Consider the highest power of X in the product $\displaystyle p p^{-1} $.

Can anybody give me a hand with this, any help would be much appreciated. I can't think why considering the highest power of x would help me