Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

Post a reply

Go back

Write your message and submit
:) :| :( :D :o ;) :/ :P :lol: :mad: :rolleyes: :cool: | :dizzy :eek :kiss :roflol :rolleyes :shame :down :up :touched :sleep :wave :swear :tongue :what :faint :dunno
Options

Go back

Topic review (newest first)

noelevans
2012-10-23 10:34:15

Hi !

Yes, generally most mathematicians tend to agree that complex numbers cannot be compared by
"greater than" or "less than" relations  (at least not in a useful, meaningful manner).  But such
a relation can, I believe be defined, though perhaps not in terribly useful manner.

Here's a shot at it.  I'll use Q for "theta" since theta isn't on the keyboard.
       iQ
In re    consider r nonnegative and Q in the interval [0degrees,360degrees).
So r is the distance from the origin and Q is the angle involved.

Given two complex numbers z and w we define
   1) z is less than w if z is closer to the origin:
   2) if z and w are the same distance from the origin then
       a)  z = w if their angles are the same.
       b)  z is less than w if z's angle is less than w's angle.

Of course if we let the r be negative and/or the angles to be any positive or negative angle, then
we weave a more tangled web.

smile

bobbym
2012-10-22 21:14:01

Hi;

Two complex numbers can not be compared.

We cannot say as they stand  that 3 + 4i is greater than 2 + 2i. But we can compare them by taking their absolute value or magnitude.

Harold
2012-10-22 21:02:48

So,is there a way to make complex number inequallity?

bob bundy
2012-10-22 18:49:58

hi Harold

But beware:



Bob

Harold
2012-10-22 18:20:13

Then, -1>-9 => i<3i,so square root of nagetive number changes inequality sign?

zetafunc.
2012-10-22 18:13:56

Yes, that is correct.

Harold
2012-10-22 18:06:00

I mean is this correct 3i>i?(for example)

zetafunc.
2012-10-22 17:41:09

What do you mean exactly?

Harold
2012-10-22 15:32:32

Is there a way to make inequality of imaginery numbers?if there is please show a example.

Board footer

Powered by FluxBB