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4i = -4
i = -4/4
i = -1
4i² = -16
4 x -1^2 = -16
16 = -16
lol I think my brain just malfunctioned upon reading that.
I agree that i = -1 is not an accurate equality, but am considering it a real representation of the imaginary.
I do not get how 4 + 4i = 0 is not equivalent to 4i = -4.
When I see an expression like 4 + j4 I see a complex number IE it has a real and imaginary component so those two numbers cannot be simply added as they describe points on 2 axes displaced 90 degrees from each other.
So you can't simply drop the real part of the expression without first determining how it will effect the imaginary part. You need to think of it as if it were really 0+4i=-4.
IE real and imaginary numbers exist on their own unique planes so mixing them is like mixing apples and oranges so what you get is a mush that's neither one nor the other (tastes good though).
Could this help account for the sign reversal?
But I don't believe it's impossible to "mix" real and imaginary numbers, if we simply think of them as normal numbers which behave differently when operated on.
all you need to do is find the square root of positive 9 and than convert it to the imaginary representation of the same number, which would be 3i, and that is the correct answer to the square root of -9 if you solve it algebraically.
Originally posted by ChaoticOrder
There is no number on the real or imaginary number line which when multiplied by its self equals an imaginary number.
...but what you have not done is explain WHY? what is the purpose of this exercise.
you've posted some videos of mathematicians and physicists proclaiming the mystery of envisioning these beasts (i assure you, they have no difficulty imagining them, they are just being generous to the uninitiated.)
in my previous post back on page 2 of this thread i gave a link to some infos about hypernumbers (wiki article here). i will reiterate to you that i think this info will be quite helpful to you in imagining what an imaginary number is.
Musean hypernumbers are often perceived as an unfounded mathematical speculation
A sign reversal is the only way that you can reach the square root of -1 or any other negative number.
We have a situation where one side of the square is negative and the other positive for some reason.
The first two levels in hypernumber arithmetic correspond to real and imaginary number arithmetic. The basis after Musès is identical to j from the split-complex numbers, and is a non-real root of . Epsilon numbers are assigned the 3rd level in the hypernumbers program.