Is every real root also a complex root? (Complex zeros and Fundamental Theorem of Algebra) Stupid question about this topic:  I don't understand the rule that says "A poly with degree N will have N complex roots".   eg:  $P(X)=x^5 + x^3 - 1$ is a 5th degree polynomial function, so P(x) has exactly 5 complex zeros.  Sorry, but how do you know it will have 5 complex zeros?  Maybe it factors into only real/integer roots?   Or, is every real root also a complex root?  ie:  $x = x + 0i$
What is a complex polynomial function (which has at least one complex zero)?  Just a poly with an "i" in the coefficient?  eg:  $4ix^2 + ...$
Disclaimer: I am not a student trying to get free internet homework help. I am an adult who is learning Calculus from a textbook. I am deeply grateful to the members of this community for their time.

Yes, real numbers are complex numbers with imaginary part $0$.
