Polynomial with complex zeroes

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

**Answer**

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

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

$(x-(i))(x-(-i))$

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

$=x^{2}+1$

$=x^{2}+1$

$x^{2}+1=0$ is one such polynomial equation