If you mean that some complex numbers are algebraic, then yes -- the imaginary unit i itself is algebraic, as it satisfies an polynomial equation x^2 + 1 = 0 wi

If you mean that some complex numbers are algebraic, then yes -- the imaginary unit i itself is algebraic, as it satisfies an polynomial equation x^2 + 1 = 0 with rational (in fact integer) coefficients. The set of algebraic numbers does not include all complex numbers, though.