Find the polynomial equation of least degree with roots - 1, 3, and (+/-) 3i

Each of these roots can be expressed as a binomial:

(x+1) = 0, which solves to - 1

(x-3) = 0, which solves to 3

(x-3i) = 0 which solves to 3i

(x+3i) = 0, which solves to - 3i

There are four roots, so our final equation will have x^4 as the least degree

Multiply them together. I'll multiply the i binomials first:

(x-3i) (x+3i) = x²+3ix-3ix-9i²

x²-9i²

x²+9 [since i²=-1]

Now I'll multiply the first two binomials together:

(x+1) (x-3) = x²-3x+x-3

x²-2x-3

Lastly, we'll multiply the two derived terms together:

(x²+9) (x²-2x-3) [from the binomial, I'll distribute the first term, then the second term, and I'll stack them so we can simply add like terms together]

x^4 - 2x³-3x²

+9x²-18x-27

x^4-2x³+6x²-18x-27