I need 2 quartic+ functions that have a complez zero.

2 answers

*Complex
if a quartic has one complex zero, it will have two. They come in conjugate pairs. An easy way to make some up is to have two quadratic factors with negative discriminants:

(x^2+4x+10)(3x^2-8x+7)
= 3x^4+4x^3+5x^2-52x+70

you can easily make up others.