Register to reply

Inequality of complex numbers

by quawa99
Tags: complex, inequality, numbers
Share this thread:
quawa99
#1
May5-14, 04:26 AM
P: 63
Are the less than (<) and greater than(>) relations applicable among complex numbers?
By complex numbers I don't mean their modulus, I mean just the raw complex numbers.
Phys.Org News Partner Mathematics news on Phys.org
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
jbriggs444
#2
May5-14, 05:33 AM
P: 965
The short answer is "no". The greater-than and less-than relations do not apply.

A longer answer is that the complex numbers together with the standard operations of addition and multiplication form a "field". But there is no greater-than relation that can be used to make it an "ordered field". http://en.wikipedia.org/wiki/Ordered_field

The problem comes when you try to decide whether i is positive or negative. i is different from zero, so it has to be either positive or negative. If it is positive then i*i must be positive. But i*i=-1 and -1 is negative. If i is negative then -i must be positive. So -i*-i must be positive. But -i*-i=-1 and -1 is negative.


Register to reply

Related Discussions
Treasure hunt using complex numbers & an inequality Calculus & Beyond Homework 45
Triangle inequality for complex numbers: sketch of proof Calculus & Beyond Homework 1
Complex Numbers Inequality Precalculus Mathematics Homework 2
Triangle inequality w/ Complex Numbers Calculus 7
Inequality and complex numbers Calculus & Beyond Homework 2