genphis said: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
genphis said: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.
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.genphis said: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.
If you increase negativity, you get something that is more negative; i.e., farther to the left of zero.genphis said:i know this goes against teachings but, if i increase negativity why does it have to turn positive.
Negative numbers are considered real. However, there are some physical quantities for which it isn't possible to have negative values, such as mass.genphis said:why are negative numbers not considered real.
It shouldn't be confusing if you understand how real numbers are laid out on the real number line, like so:genphis said: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 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.genphis said:if a temperature is -5 and then it drops 2 x as low it would then be -15 not +15
genphis said: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.
Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit, denoted by the letter i. The imaginary unit is defined as the square root of -1.
Imaginary numbers are used to represent complex numbers, which cannot be expressed as a real number. They are commonly used in fields such as engineering, physics, and mathematics to solve problems that involve quantities with both real and imaginary components.
People often confuse imaginary numbers with negative numbers because the square root of a negative number is considered an "imaginary" concept. However, imaginary numbers and negative numbers have different properties and behave differently in mathematical operations.
Imaginary numbers are a subset of complex numbers, which include both real and imaginary numbers. Complex numbers can be written in the form a + bi, where a is the real component and bi is the imaginary component. Imaginary numbers have a real component of 0, making them purely imaginary.
Imaginary numbers have practical applications in fields such as electrical engineering, signal processing, and quantum mechanics. They are also used in calculating solutions for differential equations and in the study of fractals and chaos theory.