Polynomial with complex zeroes

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Find a polynomial equation of smallest degree with a zero at $x=1-7i$.

**Answer**

Complex zeroes of polynomials come in pairs. If $x=1-7i$ is a zero of the polynomial, then the conjugate $x=1+7i$ is a zero of the polynomial too.

Thus $(x-(1-7i))$ and $(x-(1+7i))$ are factors of the polynomial.

$(x-(1-7i))(x-(1+7i))$

$=((x-1)-(-7i))((x-1)+(-7i))$

$=x^{2}-2x+1+49$

$=x^{2}-2x+50$

$x^{2}-2x+50=0$ is one such polynomial equation