From Wikipedia
In this article, the field of scalars denoted F is either the field of real numbers $\mathbb{R}$ or the field of complex numbers $\mathbb{C}$.
Formally, an inner product space is a vector space V over the field F together with an inner product, i.e., with a map
$${\displaystyle \langle \cdot ,\cdot \rangle :V\times V\to F}$$ that satisfies the following three axioms for all vectors $x$, $y$, $z ∈ V$ and all scalars $a ∈ F$
$$\cdots$$
Positive-definiteness: $${\displaystyle {\begin{aligned}\langle x,x\rangle &\geq 0\\\langle x,x\rangle &=0\Leftrightarrow x=\mathbf {0} \,.\end{aligned}}} $$
If $F = \mathbb{C}$, then $\langle \cdot ,\cdot \rangle :V\times V\to \mathbb{C}$, so $\langle x,x \rangle$ could be non-real. But then $\langle x,x \rangle \geq 0$ is meaningless because there is no order on $\mathbb{C}$.
How is the positive-definiteness condition meaningful in the case $F = \mathbb{C}$?