i is not a "trick" or a conceit to shortcut certain calculations like, say, the small angle approximation. i is a number and this must be true because of the fundamental theorem of algebra. Disbelieving in the imaginary numbers is no different from disbelieving in negative numbers.

"Imaginary" is an unfortunate name which gives makes this misunderstanding intuitive.

https://youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJ...

However, what's true about what you and GP have suggested is that both i and -1 are used as units. Writing -10 or 10i is similar to writing 10kg (more clearly, 10 × i, 10 × -1, 10 × 1kg). Units are not normally numbers, but they are for certain dimensionless quantities like % (1/100) or moles (6.02214076 × 10^23) and i and -1. That is another wrinkle which is genuinely confusing.

https://en.wikipedia.org/wiki/Dimensionless_quantity

If you take this tack, then 0 and 1 are not numbers either.