# Imaginary numbers negative confusion

1. Jan 10, 2010

### genphis

i know this must seem real stupid but if 1 x 1 =1 ( square root wise) how can -1x-1=+1 again square root wise. i am reading fermats last theorum to me if you times negative you increase the negative. i don't see why the imaginary numbers need to be invoked. i understand the argument for vectoring and working on a plane(number plane) if you are creating virtual dimensions and so on. i know i must have just missed the point please enlighten me

2. Jan 10, 2010

### Staff: Mentor

What do you mean "1 x 1 =1 ( square root wise)"? What does any of this have to do with imaginary numbers?

3. Jan 11, 2010

### genphis

hi mark44 thanks for your thread,

read page 93 fermats last theorem, where a gentlemen name bombelli created a new number called i for imaginary numbers, and you will see the connection.

i await your reply

genphis

4. Jan 11, 2010

### CRGreathouse

Essentially every poster here is aware of imaginary numbers and can calculate with them.

There is no contradiction here. $\sqrt x$ is the principle square root of x; there will be another square root. A (nonzero) number will have two square roots, three cube roots, four quartic roots, etc.

5. Jan 11, 2010

### Tac-Tics

genphis, here's the problem.

All real numbers are either positive, negative, or zero.

A positive times itself is positive.
A negative times itself is positive.
Zero times itself is zero.

But it is not possible to do a ______ times itself is negative.

Imaginary numbers are an extension of the real numbers which fill in that blank.

6. Jan 11, 2010

### genphis

hi tic tac thanks for the thread,

my bug bear is that, if i say 2 x 6 = 12 then why is -2 x -6 not -12.

i know this goes against teachings but, if i increase negativity why does it have to turn positive. why are negative numbers not considered real. if this was an energy analogy
and we were looking at symmetry negative charged-particles are as tangible as there positive counter-parts.

i think the concept of valuing -1 as a value less than 1 and not as a valid number is confusing.

if a temperature is -5 and then it drops 2 x as low it would then be -15 not +15

i know the aforementioned is rambling nonsense but it makes me wonder.

i know numbers are a system for logging and keeping track of info but the negative situation along with the imaginary numbers are perplexing.

7. Jan 11, 2010

### Staff: Mentor

Let's back up a step. Would you agree that 2 * (-6) = -12? You can also see this by adding -6 and -6 to get -12. In this case you are "increasing negativity" by doubling -6.

If you agree that 2*(-6) = -12, then it should be the case that the negative of (2*(-6)) should be the negative of (-12). IOW, -(2 * (-6)) = -(-12) = + 12.

The expression on the left side can be written as -2 * (-6) or as 2 *(-(-6)). Notice that it would be incorrect to rewrite it as (-2)*(-(-6)).

If you increase negativity, you get something that is more negative; i.e., farther to the left of zero.
Negative numbers are considered real. However, there are some physical quantities for which it isn't possible to have negative values, such as mass.
It shouldn't be confusing if you understand how real numbers are laid out on the real number line, like so:
<----(-2)---(-1) ----0------(+1) ------(+2)----->
If you take any two numbers on the real number line, the one to the left is smaller than the one to the right. So -1 < 0 and .5 < 1.1 and so on.
If a temperature is - 5 degrees (in some scale) and the temperature drops to a number twice as low, the new temp would be -10 degrees. It would not go to -15 degrees, and certainly wouldn't go all the way up to +15 degrees.

8. Jan 11, 2010

### jmsdg7

my AP Calculus teacher states that she does not like reading F(x)=-x as F(x)= "negative x" becuase saying negative x implies that the value of x is always negative in which it is not because if the variable x is negative the function is positive. She prefers to read it as "the opposite of x". If you start thinking of negative values as oposite(-6 is the opposite of 6) it can be said that taking -1X-1 is the opposite of 1 times the opposite of one which in turn is taking the opposite of the opposite of 1, which is just 1 not -1

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