A polynomial has complex roots in pairs of conjugates. As the polynomial has roots 2 and 2i, it also has -2i as a root.

The polynomial is: (x - 2)(x - 2i)(x + 2i)

=> (x - 2)(x^2 - 4i^2)

=> (x - 2)(x^2 + 4)

=> x^3 - 2x^2 + 4x - 8

**The required polynomial is x^3 - 2x^2 + 4x - 8**