Whenever there is an equation of odd degree, it certainly carries at least one real root and this is clear to me through the graphs of any odd degree polynomial since it has to change its value in the negative side hence it must go through cutting the $x-axis$. I wanted to enquire that is this also the case when the coefficients of the variable in the equation complex numbers.
For example it's clear that $$f(x)=ax^3+bx^2+cx+d$$ certainly carries at least one real root if $a,b,c,d \in R$
But is the same applicable if $a,b,c,d \in C$ where $C$ is the complex variable.