# Factorising Complex Polynomial with Complex Coefficients

I have tried to factorise the polynomial in question 19 by using the factor theorem to find other factors, however this has been unsuccessful thus far. Seeing as the conjugate root theorem does not apply to polynomials with complex coefficients, how would I go about factorising this equation given that I already know that z+i is a root? Is long division a possibility?

• You can always write out $z$ in terms of real and imaginary parts and set both equations equal to zero. – Mattos Mar 13 '15 at 10:33
• divide the given polynomial by $z+i$ and then you will get a quadratic which you can use the formula of roots – happymath Mar 13 '15 at 10:36
• Alternatively, you know you will have $3$ roots, so set $P(z) = (z - \alpha)(z - \beta)(z - \gamma)$, expand and equate. – Mattos Mar 13 '15 at 10:38