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Consider a complex vector space $V = \mathbb{C}^n$ and a quadratic form $Q(x) = x^TAx$ on $V$ where $A$ is a symmetric matrix i.e., $A^T = A$.

Is is true that the absolute value $|Q(x)|$, seen as a function $V = \mathbb{R}^{2n} \rightarrow \mathbb{R}$, is convex?

Thank you in advance for your help.

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