Incorrect description of the "cross()" function in the documentation

In the Function Description of "cross() [1/2]", it reads "With complex numbers, the cross product is implemented as (\bm a+i\bm b)\times(\bm c+i\bm d)=(\bm a\times\bm c−\bm b\times\bm d)−i(\bm a\times\bm d−\bm b\times\bm c)".

But after I tried it, I found that the right form may be (\bm a+i\bm b)\times(\bm c+i\bm d)=(\bm a\times\bm c−\bm b\times\bm d)−i(\bm a\times\bm d+\bm b\times\bm c).

By the way, I'm curious why "cross" is defined in this form as \bm a.\text{cross}(\bm b) = \bm a^*\times \bm b^* because I think it's more common to define it as \bm a.\text{cross}(\bm b) = \bm a\times \bm b.