Order relation “greater than’’ and “less than” are not defined for complex number. Give reason.
Answers
Answer:
For example, could one say that 5+2i>35+2i>3 because the real part of 5+2i5+2i is bigger than the real part of 33? Or is it just a senseless statement?
For example, could one say that 5+2i>35+2i>3 because the real part of 5+2i5+2i is bigger than the real part of 33? Or is it just a senseless statement?Can it be stated that, say, 20000i20000i is bigger than 66 or does the fact that one is imaginary and the other is natural make it impossible to compare their 'sizes'?
For example, could one say that 5+2i>35+2i>3 because the real part of 5+2i5+2i is bigger than the real part of 33? Or is it just a senseless statement?Can it be stated that, say, 20000i20000i is bigger than 66 or does the fact that one is imaginary and the other is natural make it impossible to compare their 'sizes'?It would seem that the 'sizes' of numbers of any type (real, rational, integer, natural, irrational) can be compared, but once imaginary and complex numbers come into the picture, it becomes a bit counter-intuitive for me.
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Answer:
For example, could one say that 5+2i>35+2i>3 because the real part of 5+2i5+2i is bigger than the real part of 33? Or is it just a senseless statement?
For example, could one say that 5+2i>35+2i>3 because the real part of 5+2i5+2i is bigger than the real part of 33? Or is it just a senseless statement?Can it be stated that, say, 20000i20000i is bigger than 66 or does the fact that one is imaginary and the other is natural make it impossible to compare their 'sizes'?
For example, could one say that 5+2i>35+2i>3 because the real part of 5+2i5+2i is bigger than the real part of 33? Or is it just a senseless statement?Can it be stated that, say, 20000i20000i is bigger than 66 or does the fact that one is imaginary and the other is natural make it impossible to compare their 'sizes'?It would seem that the 'sizes' of numbers of any type (real, rational, integer, natural, irrational) can be compared, but once imaginary and complex numbers come into the picture, it becomes a bit counter-intuitive for me.