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 A_j or complex numbers a_j (the affixes of the points),
• the elements of the second list (resp column) are real coefficients $\alpha_{j}^{}$ such that $\sum$$\alpha_{j}^{}$ $\neq$ 0.

barycentre returns the barycenter point of the points A_j weighted by the real coefficients $\alpha_{j}^{}$. If $\sum$$\alpha_{j}^{}$ = 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