How should complex numbers be rendered?
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20-08-2019 - |
Question
Mathematics naive question:
What is the "canonical" way to represent 14+1i?
14+i1
or
14+i
Similarly, is it likely, in the 'real world', that scientific notation is going to creep into a complex number so as to freak out a complex numbers parser? For example,
1.2345E+02-1.7002E-09i
Edit: Finally, is it
8.45358210351126e+066i
or
8.45358210351126e+66i
i.e. does one zero file to three digits on the imaginary?
Solution
No problems with MATLAB:
>> 5+i
ans =
5.0000 + 1.0000i
>> 5+1i
ans =
5.0000 + 1.0000i
>> 1.2345E+02-1.7002E-09i
ans =
1.2345e+002 -1.7002e-009i
I think this shows that scientific notation ("E
") in complex numbers is handled pretty well in the "real world"... to the extent that MATLAB is an influential part of that world =)
OTHER TIPS
My preference would be:
14 + i
Somehow it's more pleasing to my eyes than 14 + 1i.
I would represent your first example as:
14 + 1i
And I would certainly expect to see scientific notation in complex numbers. For example, Python happily accepts the following (using j
as Python requires):
>>> 1.2345E+02-1.7002E-09j
(123.45-1.7002e-09j)
"14 + 1i" is better than "14+i1", but I'd be more likely to say or write "14 + i".
Also, 1.7002E-09i
(which I haven't seen in Maths, though no doubt it happens in engineering or something) looks a bit ambiguous without a superscripted font (do you mean 1.7002*(10 ** -9)*i
or 1.7002*(10 ** -9*i)
?) and therefore (1.7002E-09)i
might be better.