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**1. The problem statement, all variables and given/known data**

Show that the function f(z) = Re(z) + Im(z) is continuous in the entire complex

plane.

**2. Relevant equations**

**3. The attempt at a solution**

I know that to prove f(z) is a continuous function i have to show that it is continuous at each part of its domain.

I take it that means i have to prove that Re(z) and Im(z) are continuous, however i have tried reading through my notes on how to do this and havn't been able to come up with a starting point.