Complex Numbers

no... because there is no such ting as infinity being a number ______________________________________________________________ Contributer 2: That's a right answer from contributer 1. But if you are really paranoid and desperately want to find out what infinity is, prepare to have your mind blown. This is not real #'s we are talking about. x/0 would equal infinity and -x/o equals negative infinity. We are assuming 0 is the threshold. This is not incorrect, simply very advanced.

The absolute value of a complex number is it's magnitude (distance from the origin). Think about complex numbers graphically, with reals on the horizontal axis, and imaginaries on the vertical axis. Now you have a right triangle: From the origin move to the right 5 units, then move down 12 units. The absolute value, or magnitude, is the length of the hypotenuse.

For this triangle, it is 13: sqrt(5^2 + 12^2) = sqrt(25+144) = sqrt(169) = 13. For magnitudes, we are only interested in the positive square root.

Lets try z^-1 which is 1/z. Now z=x+iy then 1/z = 1/(x+iy). This is equal to

(x-iy)/((x+iy)(x-iy)) and is equal to (x-iy)/(xx+yy). The real part is u=x/(xx+yy) and the imaginary part is -y/(xx+yy). Don't forget that i squared is -1 when working out (x+iy)(x-iy). Get a good program like Mathmatica as higher exponents get real time consuming and will cause brain damage!

Netflyer

For a complex number in polar form with Magnitude, and Angle:

(Magnitude)*(cos(angle) + i*sin(angle)) will give the form: a + bi

An imaginary number is a number that cannot exist. An example of an imaginary number would be: the square root of negative nine, or any negative number.

When I try to think of any two of the same numbers that would multiply together to be negative nine, all I can think of is 3 or -3. when I square both of those numbers, I get the number 9, not -9. When I multiply two negatives together, I get a positive number, therefore there is no possible way to get the square root of -9, or any negative number.

W.R.Hamilton

The idea of graphing complex numbers was published by Argand in 1806. See related link.

The set of complex numbers includes the set of real numbers. The real number system is just with the imaginary part set to 0.

example: z = 5 + i0 = 5

So the simple answer would be (2+i0)*(5+i0) = 10, so the complex values (2,0) and (5,0) get the result your looking for.

If you want a pair not on the real line then 2*exp(i*pi/4) and 5*exp(-i*pi/4) will do.

If you multiply the two complex numbers you get 2*5*exp(i*(pi/4-pi/4)) which is just 10.

Since pure imaginary numbers are also part of the set of complex numbers, you could have -2i * 5i, the i's multiplied together yield -1 and multiplied by -10 = 10.

A complex number is any number that is in the real/imaginary plane; this includes pure reals and pure imaginaries. The difference between two numbers inside this plane is never outside this plane; therefore, yes, the difference between two complex numbers is always a complex number. However, the difference between two numbers that are neither purely imaginary nor purely real is not always necessarily a number that is neither purely imaginary nor purely real. Take x+yi and z+yi for instance, where x, y, and z are all real: (x+yi)-(z+yi)=x+yi-z-yi=x-z. Since x and z are both real numbers, x-z is a real number.

The related link shows a set of complex numbers that depict the Electro-Magnetic

fields around two wires. The formula is (z-1)/(z+1)

First, let's make sure we are not confusing imaginary numbers with complex numbers.

Imaginary (sometimes called "pure imaginary" for clarity) numbers are numbers of the form ai, where a is a real number and i is the principal square root of -1.

To multiply two imaginary numbers ai and bi, start by pretending that i is a variable (like x).

So ai x bi = abi2. But since i is the square root of -1, i2=-1. So abi2=-ab.

For example, 6i x 7i =-42.

5i x 2i =-10.

(-5i) x 2i =-(-10)= 10.

Complex numbers are numbers of the form a+bi, where a and b are real numbers. a is the real part, bi is the imaginary part.

To multiply two complex numbers, again, just treat i as if it were a variable and then in the final answer, substitute -1 wherever you see i2.

Hence (a+bi)(c+di) = ac + adi + bci + dbi2 which simplifies to ac-db + (ad+bc)i.

For example:

(2+3i)(4+5i) = 8 + 10i +12i + 15i2= 8 + 10i + 12i - 15 = -7 + 22i

It is an algorithm.

The word REAL starts with the letter R!

Yes they are. They can be used to depict fields around high voltage wires.

See the below related link for the field (z-1)/(z+1).

The set of complex numbers consists of real numbers and imaginary numbers (multiples of the square root of -1), and then a combination of the two sets of numbers. Complex numbers are often depicted graphically, with real numbers on the horizontal axis, and imaginary numbers on the vertical axis. See related link for more information.

In this case, they can help visualize the electromagnetic field around wires

carrying current by the formula (z-1)/(z+1)

Refer to the related link.

Although most of us do not use imaginary numbers in our daily life, in engineering and physics they are in fact used to represent physical quantities, just as we would use a real number to represent something physical like the length of a stick or the distance from your house to your school.

In general, an imaginary number is used in combination with a real number to form something called a complex number, a+bi where a is the real part (real number), and bi is the imaginary part (real number times the imaginary unit i). This number is useful for representing two dimensional variables where both dimensions are physically significant. Think of it as the difference between a variable for the length of a stick (one dimension only), and a variable for the size of a photograph (2 dimensions, one for length, one for width). For the photograph, we could use a complex number to describe it where the real part would quantify one dimension, and the imaginary part would quantify the other.

In electrical engineering, for example, alternating current is often represented by a complex number. This current requires two dimensions to represent it because both the intensity and the timing of the current is important. If instead it were a DC current, where the current was totally constant with no timing component, only one dimension is required and we don't need a complex number so a real number is sufficient. The two key points to remember are that the imaginary part of the complex number represents something physical, unlike it's name implies, and that the imaginary number is used in complex numbers to represent a second dimension.

Remember, a purely imaginary voltage in an AC circuit will shock you as badly as a real voltage - that's proof enough of it's physical existence. I'll put a link in the link area to a great interactive site (it's actually my site but for it's educational purposes only) that explains the imaginary number utility more visually with animations.

There is no one person who invented it there are several people who had contributed.

Complex numbers, Real numbers, Rational numbers, Integers, Natural Numbers, Multiples of an integer.

Each calculator has its own nomenclature for working with imaginary and complex numbers. Many scientific calculators allow you to just type -1 and hit the square root button and it will give you something like (0,1) or (1,∠90°). In the first example, the first number {the 0} represents the real part, and the second number {the 1} represents the imaginary part. This is what happens on the HP-48 and HP-50 in Rectangular mode. In the second example, the calculator is in Polar mode (degrees), rather than Rectangular. So the first number {1} is the magnitude, and the second {90°} is the angle, measured in a counterclockwise direction from the positive real axis. 90° points straight up and is purely imaginary.

If my calculator was in radians mode, rather than degrees, then it would show (1,∠1.57) 1.57 radians is pi/2 (to 2 decimal places), which is the same angle as 90°.

An earlier calculator that I had, you first had to put the calculator in complex mode, then you had to push an extra button to view the imaginary part of the answer.