We provide an inequality for absolute row and column sums of the powers of a complex matrix. This inequality generalizes several other inequalities. As a result, it provides an inequality that compares the absolute entry sum of the matrix powers to the sum of the powers of the absolute row/column sums. This provides a proof for a conjecture of London, which states that for all complex matrices $A$ such that $|A|$ is symmetric, we have $sum(|A^p|) \le \sum_{i=1}^n r_i(|A|)^p$.