After these first two responses, I’m tempted to write something like this: “While complex numbers are theoretically possible here, unless quantum superpositions and eigenstates are important to what is being asserted, the imaginary component will be so small as to be negligible, and should be discarded.”
So far, I haven’t seen any reason to think that complex numbers are, in fact, theoretically possible there. Quantum mechanics does involve certain things called “probability amplitudes”, which can be non-real, but probability amplitudes aren’t probabilities.
It’s not that the imaginary parts are small—they’re defined on a range 2π wide (if you’re working in natural logs, and some weird width otherwise). It’s that they’re hard to interpret, and if you know (and need to know) enough to be working with them there’s little point to taking the log.
After these first two responses, I’m tempted to write something like this: “While complex numbers are theoretically possible here, unless quantum superpositions and eigenstates are important to what is being asserted, the imaginary component will be so small as to be negligible, and should be discarded.”
So far, I haven’t seen any reason to think that complex numbers are, in fact, theoretically possible there. Quantum mechanics does involve certain things called “probability amplitudes”, which can be non-real, but probability amplitudes aren’t probabilities.
It’s not that the imaginary parts are small—they’re defined on a range 2π wide (if you’re working in natural logs, and some weird width otherwise). It’s that they’re hard to interpret, and if you know (and need to know) enough to be working with them there’s little point to taking the log.