Avoid unnecessary parentheses for Units with complex value when using `format`

[adrfantini]

Describe the bug
Some units are considered complex units, meaning they are treated differently to normal, "numeric" units.
This for example is the case for the volt-ampere reactive, considered to be VAR by mathjs.

To Reproduce
I am unsure why, but converting these units leads to unexpected results:

(new Unit(1, 'MW')).to('kW').format() // 1000 kW - correct
(new Unit(1, 'MVAR')).to('kVAR').format() // (1000) kVAR - weird
(new Unit(1, 'MVAR')).to('kW').format() // (1000i) kW - weird

I understand the want to represent these as complex numbers, but I think this is fairly out of place when dealing with units. It leads to unexpected conversions and format outputs.

Notice that using formatUnits avoids this, of course, since only the number part is affected by this:

(new Unit(1, 'MVAR')).to('kVAR').formatUnits() // kVAR
(new Unit(1, 'MVAR')).to('kW').formatUnits() // kW

[gwhitney]

It is true that constructing even just math.unit(1, 'VAR') produces a Unit with a Complex value type (in this case, the value is 1+0i and the unit is VAR. And indeed, .toString() on this unit produces (1) VAR. The prettyprinter is taking care with parentheses of the fact that if the value had both real and imaginary parts, it would have no choice but to write e.g. (1 + i) VAR because 1 + i VAR would mean something different. So perhaps the solution is just to enhance the prettyprinter to know that if the unit value is Complex but only has a real part, or only has an imaginary part, the parentheses are not necessary and should not be generated. Does that sound workable on your end?

[adrfantini]

It is true that constructing even just math.unit(1, 'VAR') produces a Unit with a Complex value type (in this case, the value is 1+0i and the unit is VAR. And indeed, .toString() on this unit produces (1) VAR. The prettyprinter is taking care with parentheses of the fact that if the value had both real and imaginary parts, it would have no choice but to write e.g. (1 + i) VAR because 1 + i VAR would mean something different. So perhaps the solution is just to enhance the prettyprinter to know that if the unit value is Complex but only has a real part, or only has an imaginary part, the parentheses are not necessary and should not be generated. Does that sound workable on your end?

Yeah, I think that would be enough.

I have to say that I sincerely do not think that having complex units is useful and, in fact, can complicate things a bit for the user; however I do not have the full MathJS picture in mind and I'm sure there are excellent reasons to keep them (even just for backwards compatibility reasons, I guess).

[gwhitney]

I don't (much) use units in mathjs and am no physics/engineering expert, so I can't judge the utility of allowing complex number values for Unit quantities in mathjs; hence I am not inclined to make any effort toward their removal, given that they are already there. Also many articles found by searching "circuit analysis complex numbers" refer to representing impedance as a complex number with unit ohms, so it seems as though there does exist some use for it... However, I agree with the goal of not including parens in the string representation complex unit value when the complex number is actually real or pure imaginary, so leaving this issue open as an indication that should be done when someone has the motivation and opportunity. Thanks!

[josdejong]

I made a small PR addressing this issue: #3628

@adrfantini or @gwhitney can you maybe have a look at it?