  We study sums of $k$-potent matrices. We show the conditions by which a
complex matrix $A$ can be expressed as a sums of $k$-potent matrices. Also we
obtain conditions by which a complex matrix $A$ can be expressed as a sum of
finite order elements. This generalize some results obtain by Wu. Also we study
the sum of $k$-potent matrices in $\mathcal{M}_{\mathcal{C}f}(F)$ with $F$ be a
field and proof that any matrix in this space can be expressed as a sum of $14$
$(k+1)$-potent matrices preserving the result obtain by Slowik.
