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Because an imaginary number is impossible otherwise. For instance, the square root of negative nine (-9) is an imaginery number because any two numbers multiplied by each other yield a positive number. So the SQR of -9 must have a rational part (SQR(9)) and an imaginary part, which assigns the negative.
A:Computers work on a binary system, and western maths is based on + and _. But if there was a third category, called neutral, then the square root of minus one would be neutral 1. And the whole strange notion of imaginary numbers would be unnecessary. There are questions which can't be answered by 'yes' or 'no', when neither is applicable. In China, the answer to a question such as "Have you stopped beating your wife?" would be wumu, meaning both yes and no or neither. On a 2-dimensional graph, + is to the right, - to the left of the upright line. And neutral sticks up off the paper from zero to your eye. In a third dimension.The concept of imaginary numbers doesn't exist in China, because they think differently. We can put weights on both pans of a balance (back weighing). Or, if you have a series of rooms, each with normally always two chairs, and then take one away in one room, we would say that room now has one chair. But in China, they would say it has minus one, since it is one less than normal. It is merely a different way of thinking.
Correction:The concept of imaginary numbers does in fact exist in China, and pretty much everywhere else that has bothered to investigate along these lines of inquiry. China, a major contributor to international math, especially over at least the last 100 years, is completely aware of the concept and application of imaginary numbers.Additionally, because something has two component parts does not make it an example of westernized dichotomism as a philosophy; it simply means something has two (or one, or three) parts -- nothing more.
As to computers having two states: zero and one, this is an artifact of the means by which technology evolved, specifically electrical states of off and on, which are easy to detect, as opposed to analog electrical states, which require a lot more control and instrumentation (consider the relative complexity of a voltage meter versus a wall switch as an example). I should add that China, who is now accountably a world leader in some aspects of computer systems design, is certainly adept and comfortable with binary math and boolean algebra.
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How do you solve the power of an imaginary number?
It helps to think about imaginary and complex numbers graphically. Euler's Formula (see related link): eiΘ = cos(Θ) + i sin(Θ) {Θ is in radians}. Note that both eiΘ and [cos(Θ) + i sin(Θ)] have a magnitude of 1, so multiply by the magnitude: AeiΘ = Acos(Θ) + Ai sin(Θ). You now have a graphical representation of complex numbers, with real numbers on the horizontal axis, pure imaginaries on the vertical axis, and all other complex numbers placed on the 'complex plane'. The angle is a direction, from the origin, and the magnitude A tells how far away from the origin that the position is. With pure imaginary numbers you can have Θ = pi/2 radians (90°, vertical), and let A be either positive or negative (up or down). From the rules for exponents and powers, you now have the imaginary number z = ei*pi/2, and (ex)n = ex*n, so zn = (ei*pi/2)n = ei*n*pi/2 , so switching to degrees for simplicity: n Θ 0 0° (Points to the right: positive real) 1 90° (Pointing straight up: imaginary positive number) 2 180° (Points to the left: real negative number) 3 270° (Points straight down: imaginary negative) 4 360° (Points to the right: real positive ), same as 0° Note it goes in a circle and repeats. Odd integer values of n will be pure imaginary and even integers will be real numbers. Non-integers will put the angle so it is a complex number. Negative exponents cause it to move in a clockwise direction on the circle, rather than counterclockwise (for positive exponents). Now that you know the direction, you only need to take An, as a power, and then point it in the proper direction. So if the power of A yields a positive number, the answer will be in the direction, but if it yields a negative number (odd integer powers of a negative A), then it's in the opposite direction (add 180° to the angle).
Is 14 an integer?
An integer is any number that is positive or negative. Basically, an integer is a number.
What is the smallest negative perfect square that is divisible by the four smallest prime numbers?
Perfect squares are positive. A smallest negative number doesn't exist. The four smallest prime numbers are 2, 3, 5 and 7. The smallest perfect square would have to be 2^2 x 3^2 x 5^2 x 7^2 or 44,100
How do you divide integers?
To divide negative and positive numbers, first, look at the signs (= or -) If there is -__divided by -__, that will equal +___.So, same equal positive... and different equals negative.EX.-9 dvided by +3= -3 (different signs, negative answer)+9 divided by -3 = -3 (different signs, negative answer)+9 divided by +3= +3 (same signs, positive answer)-9 divided by -3= +3 (same signs, positive answer)Something that my teacher taught us to help us remember whether it would be positive or negative was the Love-Hate Theory.Love=PositiveHate=NegativeIf you have a positive number divided by a negative number, that would be Love and Hate, so if you love to hate, than that is basically hating, which is negative. Negative divided by a negative would be hate to hate, which is love, so positive. If you need more help, post something on my message board. Sara Mariepositive divided by a positive=positivepositive divided by negative=negativenegative divided by negative=positive (i know crazy isn't it!)
Why do you need imaginary numbers?
because somtimes there isn't an answer to every equation like what's the square root of -16.... there is no answer so we would just use an imaginary number which is i.It turns out that these are important in a practical sense. Imaginary numbers turn up all the time in quantum mechanics and certain types of electronic circuits as well.
