I was effectuating exercise #40 of chapter 1 in Schaum's outlines on Complex Variables. The question asks for the acute angle between $z_1=3-4i$ and $z_2=-4+3i$. Then using the definition $$\cos \theta={z_1 \circ z_2 \over \left|z_1\right| \left|z_2\right|}=-24/25=-.96$$ But then the author takes the angle as
$\cos^{-1}.96=16^\circ 16'$ approximately.
However, using the arccosine identity, $\cos^{-1}(-x)=\pi-\cos^{-1}x$. Besides, if we draw the actual vectors, we see that the vectors lie on opposite quadrants of the plane, which confirms this.
Therefore I ask, is there a different meaning in $\mathbb{C}$ for the angle between vectors than in high school trigonometry? Was the author justified in their actions in this example?
Also, how are angles between vectors generalized to $\mathbb{R}^n$, is there a geometric meaning behind it? From what I've learned, the definition is the same in linear algebra, but I don't know what it actually represents.