Question

How do you write the simplest polynomial of least degree with zeros i, and 2i?

Answer 1

Depending on what is meant by "simplest", `x^2-3ix-2` or `x^4+5x^2+4`

Explanation:

For the least degree polynomial (with complex coefficients) use

`(x-i)(x-2i) = x^2-3ix-2`.

If we need real coefficients, then, since `i` is a zero, its conjugate `-i` must also be a zero. And similarly for `2i` and `-2i`.
In this case the polynomial is

`(x-i)(x+i)(x-2i)(x+2i) = (x^2+1)(x^2+4) = x^4+5x^2+4`