Ordering Complex Numbers

Question

I am currently writing a piece of code that will order complex numbers, however I am not sure how to order them. For example, if I am given the numbers: 6, 3+4i, -4, 1+i and 0, how would these be ordered?

Is it sufficient just to take the magnitude of each number and order them that way?

Thanks for the help.

By magnitude you mean absolute value? Then we will have to agree that $-5>2$. Also, what will be bigger-$1$ or $i$? — Mark, Jun 20 '19 at 15:55
taking the magnitude loses the distinction between $1$ and $i$ for example — J. W. Tanner, Jun 20 '19 at 15:55
There is not a good order on the complex numbers as in the reals. You could use lexicographic ordering on the real and imaginary part, or on modulus and argument, if you prefer. — mlainz, Jun 20 '19 at 15:56
complex numbers can be ordered, but not compatibly with field operations (addition, multiplication) — J. W. Tanner, Jun 20 '19 at 15:58

score 0 · Answer 1 · answered Jun 20 '19 at 15:55

0

This depends entirely on your implementation. Note that when using magnitude for ordering that different elements can have the same magnitude. E.g. $i$ and $1$.

answered Jun 20 '19 at 15:55

Ruben

2,082

score 0 · Answer 2 · answered Jun 20 '19 at 15:59

It's up to you, since there is no standard ordering in the complex field. You could order them by magnitude, or you could - for example - use the lexicographic order: w > z if the real part of w is bigger than the real part of z. If the two real parts are equal, w > z if the imaginary part of w is bigger than the imaginary part of z.

Ordering Complex Numbers

2 Answers2