Question

What is a complex polynomial?
What is a even/odd complex polynomial?
Please, help

Answer 1

Polynomial with complex coefficients, I think.

Answer 2

That's it? I search but have no result. :(

Answer 3

Even means \(f(-x) = f(x)\) and odd means \(f(-x) = -f(x)\)

Answer 4

In either case, it must be \(f(0) = 0\) for a function to be even or odd.

Answer 5

My problem is : Prove either even or odd complex polynomial is a subspace of complex polynomial vector space. :( But I even NOT know what they are)

Answer 6

@wio, give me some suggestion, please

Answer 7

I just gave you the definitions of what they are.

Answer 8

Now you need to use the definition of vector subspace

Answer 9

yes, thanks for that, I will work on the proving problem by + and *

Answer 10

I don't see the different between real and complex coefficients in polynomials in the case.
even/odd polynomial relate to variable only, right? f(-x) = -f(x)

Answer 11

and the coefficient can change the value of the function, not change the property of odd/even
odd + odd = odd in both real and complex polynomial, right?
so, why do they ask me to prove it in complex ? is there any thing different? I doubt myself.

Answer 12

scalar k*even = even, that's it.
That's why I make a dumb question like this.

Answer 13

I dunno

Answer 14

Likely the proof for the real case is very similar.

Answer 15

yeah!!! I confused everything:(

Answer 16

Thanks for being here @wio