Question

How do you write a polynomial equation of least degree given the roots 6, 2i, -2i, i, -i?

Answer 1

`z^5-6z^4+5z^3-30z^2+4z-24=0`

Explanation:

`(z-6)(z-2i)(z-(-2i))(z-i)(z-(-i))=0`
`(z-6)(z-2i)(z+2i)(z-i)(z+i)=0`
`(z-6)(z^2-2zi+2zi-4i^2)(z^2-zi+zi-i^2)=0`
`(z-6)(z^2+4)(z^2+1)=0`
`(z-6)(z^4+4z^2+z^2+4)=0`
`(z-6)(z^4+5z^2+4)=0`
`z^5-6z^4+5z^3-30z^2+4z-24=0`