Barycenter of complex numbers : barycentre

### 5.11.10 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 :
affix(barycentre(...,...)) because barycentre(...,...) returns a point, not a complex number.
Input :

affix(barycentre([1+i,1-i],[1,1]))

or :

affix(barycentre([[1+i,1],[1-i,1]]))

Output :

i