Does the concept of greater-than / less-than carry over from real / imaginary numbers to complex numbers? If so, how do you determine if one complex number is greater than or less than another?

peasypod

Here's something for you to think about: A complex number is any number in the form a + ib, where a and b are real numbers and i is the square root of -1; a and ib are respectively the real and the imaginary part of the number. Setting a or b equal to zero gives an imaginary and a real number respectively. So, we are back to the zero concept...Have I confused you now?!? Oct 27 04, 6:44 PM

gmackematix

The complex numbers can be matched to points in a plane. Now would you say the point (1,2) is more or less than the point (2,1)? Oct 27 04, 7:38 PM

mikeBarr81

You could posibly represent them using polar coordinates and use the magnitude of the number (radius of the circle it falls on) to determine which number was greater. Problem is, that would make 1 = -1 etc.... Maybe this could be solved using angle, the greater the angle, the less the number? Again, the problem is that the number 1 has an angle of 0, but just as validly has an angle of 360 degrees (or 2PI radians if you will), or any multiple of this. Oct 27 04, 8:10 PM

gmackematix

You could do an ordering by putting them in order of the real part and if those are the same in order of the imaginary part. But does it seem right that 1000i should be less than 1? The truth is that there is no unique ordering of the complex numbers (or points in a plane) like there is with the real numbers so in answer to the question, > and < are not well-defined properties in the world of complex numbers. Oct 27 04, 8:58 PM

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