  A complex harmonic polynomial is the sum of a complex polynomial and a
conjugated complex polynomial, of degrees $n$ and $m$ respectively. Li and Wei
(2009) presented a formula for the expected number of zeros of a random
harmonic polynomial in $\mathbb{C}$. In this paper we prove that if $m$ is a
fixed number, this expectation is asymptotically $n$ as $n\rightarrow\infty$,
and if $m=n$ we find a lower and upper bound of order $n\log n$ for this
expectation for sufficiently large $n$.
