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#1 2012-10-21 16:32:32

Harold
Guest

Inequality

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

#2 2012-10-21 18:41:09

zetafunc.
Guest

Re: Inequality

What do you mean exactly?

#3 2012-10-21 19:06:00

Harold
Guest

Re: Inequality

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

#4 2012-10-21 19:13:56

zetafunc.
Guest

Re: Inequality

Yes, that is correct.

#5 2012-10-21 19:20:13

Harold
Guest

Re: Inequality

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

#6 2012-10-21 19:49:58

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,532

Re: Inequality

hi Harold

But beware:

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2012-10-21 22:02:48

Harold
Guest

Re: Inequality

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

#8 2012-10-21 22:14:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,663

Re: Inequality

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.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9 2012-10-22 11:34:15

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Inequality

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


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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