The product of two positive integers is positive. Numbers like $-1 + i$ and $1 - i$ are called "associates," but since they have the same norm, it's not of much concern which one is in which quadrant. Suppose you have two numbers 20 and -4 and wish to divide the first integer by the other. If both of your numbers are negative, the result is positive because the two negatives cancel out the others. $1 - 3 \sqrt$, for example) is either $0$ or a positive real integer.
You can always use one with or without the other. Similarly, $-i$ is a purely imaginary number but we could say it has a negative imaginary part, that $\Im(-i) = -1$. The positive and negative prompts are in equal footing. But one could argue that $\Im(i) = 1$ and that that is a positive number.
For example, given a positive test result, an LR of 2.0 indicates the odds are 2:1 (true positives:false positives) that a positive test result represents a patient with disease. But for the sake of clarity and not causing needless confusion, I strongly urge you to avoid using "non-positive numbers" to mean negative real numbers and complex numbers having nonzero imaginary part. For a given test, the LR is different for positive and negative results. But I suppose that theoretically you can use any term to mean whatever you want (including counter-intuitive meanings) as long as you define it. I don't think I had ever heard the term "non-positive number" used in any way whatsover.
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