Extend polynomial identities to complex numbers for higher-degree polynomial work.
Multiply complex conjugate linear factors to write a real polynomial
Problem
Expand \((x~-~(2~+~3i))(x~-~(2~-~3i))\) as a real polynomial.
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What this problem is really about
Rewrite the two factors around their shared real center so the opposite imaginary parts form a conjugate pair. Their product is a difference of squares: the imaginary cross terms cancel, and subtracting the negative square of the imaginary part adds a real constant. Expand the centered real square only after using that structure.
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