Math Is Fun Forum

Harold

Guest

Inequality

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

zetafunc.

Guest

Re: Inequality

What do you mean exactly?

Harold

Guest

Re: Inequality

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

zetafunc.

Guest

Re: Inequality

Yes, that is correct.

Harold

Guest

Re: Inequality

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Inequality

hi Harold

But beware:

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Harold

Guest

Re: Inequality

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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.

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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.