I came across a question which asks to find all polynomials $f$ over $\mathbb{C}$.
Does this mean the coefficients of the polynomial can be complex or the polynomial can take complex values?

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    $\begingroup$ it means the coefficients of the polynomial are in $\mathbb C$ $\endgroup$ – J. W. Tanner Mar 1 at 23:13
  • $\begingroup$ Are you sure the question is not asking for all irreducible polynomials over $\mathbb C$? $\endgroup$ – N. S. Mar 2 at 1:14

The polynomials over $\Bbb C$ (or more generally any field $\Bbb K$) are expressions of the form


where $X$ is an indeterminate and $p_0,p_1,p_2,...,p_{m-1},p_{m}$ are in $\Bbb C$ (or more generally $\Bbb K$).

  • $\begingroup$ What is K? ${}{}{}{}$ $\endgroup$ – Some Guy Mar 2 at 1:21
  • $\begingroup$ I use the letter $\mathbb K$ to denote any field $\endgroup$ – J. W. Tanner Mar 2 at 1:26
  • $\begingroup$ Thanks ${}{}{}{}$ $\endgroup$ – Some Guy Mar 2 at 1:27

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