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Question Number 1426 by tabrez8590@gmail last updated on 31/Jul/15
why we can not compare any tow complex number    how a cmplex number is uses a complex number practically please giveanexample
$${why}\:{we}\:{can}\:{not}\:{compare}\:{any}\:{tow}\:{complex}\:{number}\:\: \\ $$$${how}\:{a}\:{cmplex}\:{number}\:{is}\:{uses}\:{a}\:{complex}\:{number}\:{practically}\:{please}\:{giveanexample} \\ $$
Commented by Rasheed Ahmad last updated on 03/Aug/15
Things with respect to single   characteristic are easy to compare.      For example if we consider   counting of people we can easily  say that ′ This country is bigger  than that.′        But the things with more than  one characteristics are not  cmparable in general.         For example If ′counting of  people′ and ′area′ are considered  with countries we can′t say ′ This  country is bigger than that′.           In the same way the complex  numbers having two characteristics  (Real and Imag.) can′t be compared  in general.           However a characteristic  has been defined named ′modulus′  of complex number and with   respect to modulus they can be  compared.  (If we consider complex numbers  as points in Argand′s diagram (  complex plane) the modulus is  the distance of the point from  origin)          For appication pl see   advanced books of differnt  subjects.
$${Things}\:{with}\:{respect}\:{to}\:{single}\: \\ $$$${characteristic}\:{are}\:{easy}\:{to}\:{compare}. \\ $$$$\:\:\:\:{For}\:{example}\:{if}\:{we}\:{consider}\: \\ $$$${counting}\:{of}\:{people}\:{we}\:{can}\:{easily} \\ $$$${say}\:{that}\:'\:{This}\:{country}\:{is}\:{bigger} \\ $$$${than}\:{that}.' \\ $$$$\:\:\:\:\:\:{But}\:{the}\:{things}\:{with}\:{more}\:{than} \\ $$$${one}\:{characteristics}\:{are}\:{not} \\ $$$${cmparable}\:{in}\:{general}. \\ $$$$\:\:\:\:\:\:\:{For}\:{example}\:{If}\:'{counting}\:{of} \\ $$$${people}'\:{and}\:'{area}'\:{are}\:{considered} \\ $$$${with}\:{countries}\:{we}\:{can}'{t}\:{say}\:'\:{This} \\ $$$${country}\:{is}\:{bigger}\:{than}\:{that}'. \\ $$$$\:\:\:\:\:\:\:\:\:{In}\:{the}\:{same}\:{way}\:{the}\:{complex} \\ $$$${numbers}\:{having}\:{two}\:{characteristics} \\ $$$$\left({Real}\:{and}\:{Imag}.\right)\:{can}'{t}\:{be}\:{compared} \\ $$$${in}\:{general}. \\ $$$$\:\:\:\:\:\:\:\:\:{However}\:{a}\:{characteristic} \\ $$$${has}\:{been}\:{defined}\:{named}\:'{modulus}' \\ $$$${of}\:{complex}\:{number}\:{and}\:{with}\: \\ $$$${respect}\:{to}\:{modulus}\:{they}\:{can}\:{be} \\ $$$${compared}. \\ $$$$\left({If}\:{we}\:{consider}\:{complex}\:{numbers}\right. \\ $$$${as}\:{points}\:{in}\:{Argand}'{s}\:{diagram}\:\left(\right. \\ $$$$\left.{complex}\:{plane}\right)\:{the}\:{modulus}\:{is} \\ $$$${the}\:{distance}\:{of}\:{the}\:{point}\:{from} \\ $$$$\left.{origin}\right) \\ $$$$\:\:\:\:\:\:\:\:{For}\:{appication}\:{pl}\:{see}\: \\ $$$${advanced}\:{books}\:{of}\:{differnt} \\ $$$${subjects}. \\ $$$$ \\ $$

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