Note:Sorry if this is the wrong section, the course this is from is 'Complex Analysis', so I assumed it belonged here.

The question

f(z) = im(z)

Where is f continuous?

My attempt

Unless I'm mistaken, we need to show that

$\displaystyle \lim_{z \to z_0} f(z) = f(z_0)$

The limit is $\displaystyle y_0$, and f(z) is also $\displaystyle y_0$. So is the function continuous everywhere, or am I doing this incorrectly?

Thanks.