Recently in Calculus 1 we were introduced to the concept of analytic functions (to be more exact, real analytic functions). At the same time I was familiar with the concept of complex analytic functions (being defined as complex functions that are differentiable). I was wondering whether the real part of a complex analytic function is itself real analytic (ie. it has a local Taylor series expansions around any point defined in the function). And why?
the closest answer I've seen in here is the answer from Seth(user:883910) but it wasn't very clear or satisfactory to me: Real part of an analytic function
(also I'd appreciate it if details are presented (but explained at a relatively novice level if possible), and sources which give more information on this are given.)
thanks.