Complex Numbers

Ah! but they can. Using absolute values |3-i|<|3+2i|.

If I understand the question correctly, it is when the algebraic equation (or inequality) is true.

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A complex number can be a pure imaginary, or a pure real number, or a combination of the two. The form for a complex number is a + bi, where a & b can be any real numbers (so if a = 0, then the number is pure imaginary; and if b=0, then it is a real number).

See the related link Answers dot com video for some examples of how to solve.

No. Dividing by zero is undefined. It does not result in anything.

I am not sure. I am not to good at minecraft.

One use is to compact a large area into a small one or vice versa. The complex

formula is 1/z, which is inversion. All pairs of complex numbers with absolute value less than 1 will be transformed outside the unit circle and the infinite complex plane will be compacted inside the unit circle! This simple formula produces the real part u=x/(xx+yy) and imaginary part v=-y/(xx+yy). Points approaching infinity will go to zero inside the unit circle!

62% or 62/100

Complex numbers are not used in everyday life, unless you work in some very specific areas, including electrical engineering, or nuclear physics, where those numbers are required, or want to work with fractal art, for example.

Complex numbers are not used in everyday life, unless you work in some very specific areas, including electrical engineering, or nuclear physics, where those numbers are required, or want to work with fractal art, for example.

Complex numbers are not used in everyday life, unless you work in some very specific areas, including electrical engineering, or nuclear physics, where those numbers are required, or want to work with fractal art, for example.

Complex numbers are not used in everyday life, unless you work in some very specific areas, including electrical engineering, or nuclear physics, where those numbers are required, or want to work with fractal art, for example.

No, it is not.

Hul Gu, better known as Hulagu Khan and also known as Hulagu, Hülegü, or Hulegu. (c. 1217 - Febuary 8, 1265), was a Mongol ruler who conquered much of Southwest Asia. Son of Tolue and the Kerait princess Sorghaghtani Beki, he was a grandson of Genghis Khan, and the brother of Arik Boke, Mongke and the great Kubalai Khan. Hulagu's army greatly expanded the southwestern portion of the Mongol Empire, founding the Ilkhanate of Persia, a precursor to the eventual Safavid Dynasty, and then the modern state of Iran. Under Hulagu's leadership, the Mongols destroyed the two greatest centers of Islamic power, Baghdad and Damascus, causing a shift of Islamic influence to the Mamluks in Cairo. It was also in Hulagu's reign that historians switched from writing in Arabic, to writing in Persian.

Multiplying any complex number by its conjugate will result in a positive real number.

For any complex number x + yi, {x and y are real numbers} its conjugate is x - yi, and the multiplication equals x2 + y2

you would use complex and imaginary numbers in your daily life if you become a mathematician, electrical engineer, quantam mechanic, etc. otherwise, you would not use use them at all except in algebra 2, pre-calc, calculus....i hope that helped a little bit.

Yes.

A complex number, z, may be written as z = x + iy where x and y are real and i is the imaginary square root of -1.

x is the real part of z and iy is its imaginary part.

The Argand diagram for z would show it as if it had the coordinates (x, y) in the Cartesian plane. However, where the Cartesian plane has the x-axis the Argand diagram has the real part, and where the Cartesian plane has the y-axis the Argand diagram has the imaginary part.

Equivalently, z can be defined in terms of polar coordinates: z = (r, q).

This is the same as z = rcosq + i*rsinq, so the real part is rcosq.

This is best done if the complex number is in polar coordinates - that is, a distance from the origin, and an angle. Take the square root of the argument (the absolute value) of the complex number; and half the angle.

Yes, for example (a + bi)(c + di) = ac + adi + bic + bidi, and commutative property works as well --> ac + adi + bci + bdi² --> ac + (ad + bc)i + bd(-1) = (ac - bd) + (ad + bc)i

• The set of Real Numbers
• The set of Imaginary Numbers

Yes. Also, for finding any other root (cubic root, fourth root, etc.).

The main square root of a complex number can be found easily if it is expressed in polar notation. For example: the square root of 5 at an angle of 46 degrees) the complex number that has the absolute value 5 and an angle of 46 degrees) is equal to the square root of 5, at an angle of 46/2 = 23 degrees.

Finding the total or summation

eix = cos(x) + i*sin(x)

where e is the irrational number 2.7182...

i is the maginary sq root of -1

and x is measured in radians.

In the special case when x = pi, this reduces to:

eiπ = cos(π) + i*sin(π)

or

eiπ = -1

It is the continuum.

Complex numbers are theoretically interesting; they help us better understand the real numbers in some cases.They also have some very practical applications, including:

* Electrical circuits - in AC, things like resistance, current, and voltage acquire a phase angle, thus becoming complex numbers.

* Quantum mechanics - the probability amplitude is described with a complex number. As a result, complex numbers basically permeate all of quantum mechanics.