Complex Numbers

It isn't clear in what form you have the complex number. But you can change it from the form (absolute value, angle) to the form (real part + imaginary part) using the polar-rectangular conversion available on scientific calculators (and the other way round, with the rectangular-polar conversion). Note that a complex number in the form (real part + imaginary part) is most appropriate for addition and subtraction, while a complex number of the form (absolute value, angle) is most appropriate for multiplication or division, so depending on the operations, you may want to convert back and forth several times.

Complex numbers can be represented as reiƟ, where r is the distance from the origin, and Ɵ is the angle (in radians) with the positive real-axis (horizontal axis).

See the answer to the related question: 'How do you solve the power of an imaginary number?' (Link below)

This depends on whether the pie is thick or not - if you mean 4 cuts from the top downwards, then you can get nine, if you cut it right. Imagine a clock face. cut 1 - from 1:00 to 5:00 cut 2 - from 11:00 to 7:00 cut 3 - from 10:00 to 2:00 cut 4 - from 8:00 to 4:00 Alternatively, with a thick pie you could make three top-downwards cuts to give six people and one through the middle of the pie, parallel to the plate, to divide each of those pieces in two - giving a total of 12 pieces. (This works when if you're dealing with 'cake' instead of 'pie'.)

Yes, the only argument would be the example, i + (-i) = 0. However, many people don't realize that 0 is both a purely real and pure imaginary number since it lies on both axes of the complex plane.

the absolute value of x + iy is equal to (x^2+y^2)^.5

and is the same for the conjugate, x-iy

All pairs of numbers, written in the form a + bi (for example: 3 + 5i, or 7 - 2i, etc.), where the first number is called (for historical reasons) the "real part" and the second number the "imaginary part". Complex numbers can be graphed as points on a plane. They have important applications in several fields of science, arts, and pure mathematics.

Yes -- one sextillion.

Also according to one scientific hypothesis, this is the estimated number for the number of stars within our current universe with the number slowly increasing as time progresses.

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.

Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.

felipe voloch

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).

i think birdman is rich than 5o cent and that is a fact i think birdman is rich than 5o cent and that is a fact

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).

Any well-defined set of numbers.

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.

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.

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.

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.