I am reading a book called College Algebra and it defines polynomials as an expression of the form $a_nx^n + a_{n-1}x^{n-1} + …+ a_2x^2 + a_1x + a_0$ where $a_j$ are real numbers ( I'll stop the definition there). Does polynomials only have real coefficients or it can be complex numbers?
I asked this on a wrong place (Cross Validated) my bad.
Best Answer
Polynomials can also have complex coefficients. There is actually quite a bit of work related to the topic. See, for example, here or here.
An example of such a polynomial would be
$$(42+42i)x^2+(7+i)x.$$
The roots of the above polynomial are at $$x=0 $$ and $$ x = -\frac{2}{21} + \frac{i}{14}.$$
So, nobody hinders you to create polynomials with complex coefficients.