Please read the
forum rules. No one here will do your homework for you. You must show some effort.
the first thing you need to work on is finding a way of representing complex numbers. I usually do that with a struct. Once you have that, the 4 operations are defined in any number of mathematics text-books or the internet. Once you have the 4 operations set up, you can use the quadratic formula to solve the polynomial equation ax^2+bx+c = 0, or use the operations to evaluate the polynomial expression ax^2+bx+c.
Just a pedantic note: ax^2+bx+c is not a polynomial equation. It is a polynomial expression, to be an equation it must contain an equals sign.
ax^2+bx+c = 0 is an equation (and probably the one you mean).
ax^2+bx+c is an expression -- and can not be solved, it may be evaluated (which might be what you mean by "solved").