Can an inner product on a vector space be negative?

This may be a noob question but I recently read a definition that an inner product on a complex vector space is said to be a positive-definite sesquilinear map.

Doesn't positive definite mean that the inner product will only return positive values?

(Just started studying Functional Analysis specifically Hilbert Spaces)

Positive-definite in this sense only means that $\langle x, x\rangle > 0$ if $x \neq 0$, it doesn't prohibit general $\langle x, y \rangle$ from being zero, negative, complex, etc.