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Math functions for arguments outside the domain should raise exception according to SQL Standard
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> The SQL standard is technically incorrect (or is geared for someone with a primary school education only).

I would add: "and overly paternalistic". Who is to say it's an error? The answer is simple: No real number. NULL is the closest approximation to that.

> SQRT(-1) -> 1j; LN(-1) -> 3.141592653589793j

I think you have revealed yourself as being trained in electrical engineering. Mathematics folks say 'i' rather than 'j'.

> ... the answer does, in fact, exist.

Only in an imaginary way. If somebody adjusts your bank balance by that amount, you need to be thinking about doing business elsewhere.