Barycenter of complex numbers : barycentre

### 2.11.10 Barycenter of complex numbers : `barycentre`

See also : ?? and ??.
`barycentre` takes as argument two lists of the same size (resp. a matrix with two columns):

- the elements of the first list (resp column) are points Aj or complex numbers aj (the affixes of the points),
- the elements of the second list (resp column) are real coefficients αj such that ∑αj ≠ 0.

`barycentre` returns the barycenter point of the points Aj weighted by the real coefficients αj. If ∑αj = 0, `barycentre` returns an error.
Warning To have a complex number in the output, the input must be :
`affixe(barycentre(...,...))` because `barycentre(...,...)` returns a point, not a complex number.
Input :

`affixe(barycentre([1+i,1-i],[1,1]))`

Or :

`affixe(barycentre([[1+i,1],[1-i,1]]))`

Output :

`i`