# Polynomial $f$ over $\mathbb{C}$.

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?

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

The polynomials over $$\Bbb C$$ (or more generally any field $$\Bbb K$$) are expressions of the form
$$p_0+p_1X+p_2X^2+\cdots+p_{m-1}X^{m-1}+p_mX^m$$,
where $$X$$ is an indeterminate and $$p_0,p_1,p_2,...,p_{m-1},p_{m}$$ are in $$\Bbb C$$ (or more generally $$\Bbb K$$).
• What is K? ${}{}{}{}$ – Some Guy Mar 2 at 1:21
• I use the letter $\mathbb K$ to denote any field – J. W. Tanner Mar 2 at 1:26
• Thanks ${}{}{}{}$ – Some Guy Mar 2 at 1:27