Question

find a fourth degree polynomial equation with integer coefficients that has the given numbers and roots: 2i and 4-i

Answer 1

first the roots are: 2i, 4-i and their pairs of -2 and 4+i
therefore the factors are x-2i, x+2i, x-4+i and x-4-i
times there using a method of your choice : (x-2i)(x+2i)(x-4+i)(x-4-i)
to get (x^4)-8(x^3)+21(x^2)-32x+68