Know the Fundamental Theorem of Algebra and connect it to polynomial roots.
Find the conjugate root of a real-coefficient polynomial
Problem
A real-coefficient polynomial has root \(3~+~4i\). State the required conjugate root.
Big Picture
What this problem is really about
Real coefficients force nonreal roots to occur in complex-conjugate pairs. Forming the conjugate preserves the real component and changes only the sign of the imaginary component; it does not negate the entire number or swap its parts. The paired factors multiply to a quadratic with real coefficients because their imaginary terms cancel.
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