Question

write a polynomial function in standard form with the given zeros. 1-2i,2

Answer 1

complex numbers, like radicals, always come in their conjugate form
so if -2i is a zero so is +2i

so f(x) = (x-1)(x-2)(x - 2i)(x + 2i)

the last two factors multiply for x^4 + 4

f(x) = (x-1)(x-2)(x^4 + 4)

expand if needed, I like it the way it is.

Answer 2

no comma there actually
zero when
x = 1-2i
x = 1+2i
x = 2
so I get
(x-2)(x-1+2i)(x-1-2i)
(x-2) (x^2-2x+5)

Answer 3

Just have to get stronger glasses.