double sum of complex numbers

Question

I have $ c_{1},...,c_{n} \in \mathbb{C} $. Can I say that: $$ \sum_{j=1}^{n}\sum_{k=1}^{n}c_{j}\overline{c}_{k} \geq 0 ? $$ Thank you.

Answer 1

$$\sum_{j=1}^n\sum_{k=1}^n c_j\overline c_k=\sum_{j=1}^n c_j\sum_{k=1}^n\overline c_k=S\overline S\ge 0, \text{ where } S=\sum_{j=1}^n c_j.$$