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Are real-analytic functions in $\mathbb{R}^2$ holomorphic after suitable change of coordinates?

I'm not sure this is a research-level question, but I couldn't find an answer after a bit of searching, so here goes. Let $f: \mathbb{R}^2 \to \mathbb{R}^2$ be a real-analytic function. Can we always ...
Mikhail Tikhomirov's user avatar