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Florian is consistent | 186 comments | Create New Account
Comments belong to whoever posts them. Please notify us of inappropriate comments.
Florian is consistent
Authored by: Anonymous on Friday, November 23 2012 @ 01:23 AM EST
What's wrong with just -i

[ Reply to This | Parent | # ]

big/small complex numbers
Authored by: Anonymous on Friday, November 23 2012 @ 04:08 AM EST
First-off please do not be intimidated by the term 'complex'
or 'imaginary' being used in this description. There is
nothing actually difficult (complex) or 'spooky' (imaginary)
intended.

My math-professor 'defused' both by presenting the following
definition for a complex number: 'A complex number is a point
in a plane'. In other words: The term complex number is only
'math-speak' for a trick performed upon a point in a plane.

One traditional representation of a point in a plane is to
use a Cartesian X/Y coordinates system in the plane. 'Math-
speak' for a plane with a Cartesian coordinates system that
is used to represent complex numbers is to call it a 'complex
plane' (please remember what i mentioned about not being
intimidated..)

For complex numbers the traditional presentation is to
present real numbers as points on the X-axis, using the
number's value as the coordinate value. Pure 'imaginary'
numbers are similarly represented as points on the Y-axis.
Y'see: nothing 'imaginary' about the number at all: it's just
a point on the Y-axis.

Complex numbers (the ones that have a non-zero both real and
imaginary part) are represented by points with X-coordinate
the real part of the number, and the Y-coordinate the
imaginary part of the number.

All 'normal' real numbers are represented as points on the X-
axis of the 'complex plane', forming a subset of the complex
numbers: the complex numbers that have an imaginary part
equal to zero.

The traditional way of ordering real numbers can be presented
in this complex plane as that real numbers to the right (in
the direction of the positive X-axis) are bigger than real
numbers more to the left on the X-axis.

If you understand the above (and if i've not messed up by
making mistakes.. :-) ), you'll understand that to order
actual complex numbers becomes a bit problematic: You can
order the real part (X-axis value) of the number, you can
analogously order the imaginary part of the complex number
(same 'trick', using the Y-axis), but what to do about the
combination?

That is why there is -generally speaking- no way to order
complex numbers as 'bigger' or 'smaller'.

[ Reply to This | Parent | # ]

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