how do you make imaginary zeros back into polynomial functions?

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First, if you only know one root such as 4 - i, then you need to have its conjugate which is found by chaning the operation in the middle. The conjugate of 4 - i would be 4 + i. Then write each term as (x - (4 - i))(x - (4 + i)) and multiply the terms together. The i terms should drop out and the i^2 term will = -1.