Complex conjugate

for real polynomials:
if x=z, a complex root then x=[Complex conjugate], complex conjugate is also a root

bros what the fuck is a complex conjugate?
looking it up it's saying to find the complex conjugate of a complex number is flip the sign for instance 4+7i --> 4-7i

but if it's a complex number why does it's sign matter? we are looking for a real number from the polynomial but doesn't it have the same real number for either i or -i, or am I retarded?

tldr

dont overcomplicate it for yourself, just know that complex conjugate of a+bi is a-bi

isnt because when you time an imaginary by its complex conjugate the imaginary should be cancelled out?

ngl i have not done this shit in a while

Regarding the complex conjugate, you flip the sign of the imaginary part of the complex number.
So if you think of complex numbers as a plane, with the x-asis as the real part and the y-axis as the imaginary part, doing the conjugate of a number is the equivalent of reflecting the point across the x-axis