How to tell where parentheses go in functional notation? The professor gave us a function $f(z) = \ln r + i \theta$ (this is for a complex analysis class). He doesn't like answering students' questions and there's no assigned textbook so I don't know where to look up such a function. How can I tell where the parentheses are supposed to go for this equation?

With an expression like this, we have three possibilities:
Either
\begin{align*}
f(x) &= \ln(r) + i\theta,\\
f(x) &= \ln(r + i)\theta, \text{ or}\\
f(x) &= \ln(r + i\theta).
\end{align*}
We can assume the professor means $\ln(r) + i\theta$, since it requires the simplest expression in parenthesis. Generally, if the expression in parenthesis is at all 'complicated' (requires any binary operations like addition, subtraction, etc), it belongs in parenthesis. If no such operations are required, parenthesis can be safely omitted and we agree to default to the simplest argument possible for the function.
That's not to say I agree with saying something is 'obvious', but I'm merely providing hints for the future!
