Consider the function \(f\left( z \right) = z + {z^*}\) where  is a complex variable and  denotes its complex conjugate. Which one of the following is TRUE?

1
\(f\left( z \right)\) is both continuous and analytic
2
\(f\left( z \right)\) is continuous but not analytic
3
\(f\left( z \right)\) is not continuous but is analytic
4
\(f\left( z \right)\) is neither continuous nor analytic

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