If the polynomial has two roots or zeros, then the least degree it can be is 2. But when x = -i is a root, generally x = i is a root too. Thus the degree here is 3. Using the roots, you can write the polynomial by finding a factor from each. The zeros are the solution to the factor. So if x = 1, it came from the factor x - 1. x = 1 is the solution because x - 1 = 0 is x = 1 solved.
When x = -i, i this is the result of a square root of a negative number. So x had the exponent 2. To write the factor for x = -i, you should write x^2 + 1. When solved x = +/-√-1 = +/- i.
