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

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

Correct answer: f(z) is continuous but not analytic

Solution

The function f(z) = z + z* is continuous because it is composed of continuous functions (the identity and conjugate functions). However, it is not analytic since it does not satisfy the Cauchy-Riemann equations, which are necessary for a function to be analytic in the complex plane.

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