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

1 Answer
May 24, 2017

Answer:

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#