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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.
What is a negative times a positive times a positive?
A negative. If you have a string of positive and negative numbers multiplied together, all you need to find the sign of the answer is to find the parity of the negative numbers. If there are an odd number of negatives then the answer is negative and if there are an even number of negatives then the answer is positive. Remember, positive numbers make no difference to the sign of the answer.
How can we find the LCM of negative numbers?
The same as with positive numbers. You need at least two numbers to find a GCF.
What are the factors that will equal negative ten?
factors are the numbers you multiply together to get a product in a multiplication problem. a positive times a positive = a positive a positive times a negative = a negative a negative times a negative = a positive since you are looking for negative 10, you need one factor to be positive and one to be negative. this could be: -1*10 -10*1 -2*5 -5*2
How is a negative times a negative a positive?
the thing is that when there are two negatives you need to cross out those which will give positive times positive equals positive. this is the rule that you need to learn it. negative*negative=positive positive*positive=positive negative*positive=negative The same thing for devision
What is negative 4 times negative 11 plus negative 22?
To multiply two numbers with negatives involved you first multiply them normally. In this case 4x11 = 44. The next step is to assess whether the answer is positive or negative. In cases where there is one negative and one positive in the multiplication, the answer will be negative. Otherwise, the answer will be positive. In this case, both numbers were negative so the answer must be positive. Thus we have 44 and need to add negative 22. Adding negative numbers is the same as subtracting those numbers. Thus the question is 44-22 = 22. Therefore, negative 4 times negative 11 plus negative 22 is 22.
Can you square an integer and get a negative number?
No. The square of a positive number is positive; the square of a negative number is also positive; and the square of zero is zero. If you want to square a number and get a negative result, you need complex numbers. For example, the square of 2i is -4.
What is the answer to negative fifteen divided by positive three?
Negative 5. It's normal division, except you need to remember these rules: Positive & Negative = Negative Positive & Positive = Positive
What are the factors of x2-8x plus 16?
x^2 - 8x + 16 = 0(x )(x )You need two numbers that when multiplied are equal to 16, and when added are equal to 8.These two numbers are 4 and 4 (4 * 4 = 16, 4 + 4 = 16)Then you need to figure out if these are positive or negative. Since 16 is positive, you know that the numbers are either both positive or both negative. Since the 8 is negative, you know they must be negative.(x - 4)*(x - 4)
What is a good rap about Negative and positive numbers?
Negative is less than 0 and positive is more, than the big '0' This you need the know for math ga-loreuh huh uh huh*repeat*
What are the negative GCF of 980?
A couple of problems. You need at least two numbers to find a GCF and the GCF is by definition positive.
Program which inputs two complex numbers and finds the sum and product of those numbers?
Try thisinput "z =?";x,yprint "z=";x;"+";y;"i"input "w =?";u,vprint "w=";u;"+";v;"i"print "z+w = ";x+u;"+";y+v;"i"print "z*w = ";x*u-y*v;"+";x*v+y*u;"i"example output:z=? 1,2w=? 2,3z+w = 3+5iz*w = -4+7iNote that it is possible to input negative imaginary parts. To display the sum and product correctly in that case, you need to make an intermediate step in the program which assigns the imaginary part to a separate variable, decide whether or not the imaginary part is negative, and then print a "+" if it is positive or no sign when it is negative (printing a negative number will automatically print the negative sign).Of course, you need to modify the program to your computer language.
What are Real and Complex numbers?
Real numbers are numbers that you are already familiar with: integers, fractions, and irrational numbers: 1, 2, 0, -5, ¾, sqrt(2), pi, etc. Next, you need to know about imaginary numbers. These are numbers that, when squared, will give a negative real number. No real number can do that. Now imagine a graphical plane, with the real axis on the horizontal, and the imaginary axis on the vertical. This is called the complex plane, and any combination of real and imaginary numbers can be plotted on the complex plane.The set of complex numbers includes all real numbers as well as all imaginary numbers, and the combination of the two.
