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Complex Numbers
The square root of negative one, which we now call the imaginary unit, was once thought to be an absurd notion. However, through the diligent studies of open-minded mathematicians, it was shown that the real numbers were actually just one part of a larger set of numbers known as the complex numbers, the other part being the imaginary numbers. Please direct all questions about these surprisingly useful and applicable numbers into this category.
887 Questions
How do you graph the addition of complex numbers?
Consider the Complex Plane, with Real numbers along the horizontal axis, and Pure Imaginary numbers on the vertical axis. Any Complex number (a + ib) can be plotted as a point (a,b) on this plane. The point can be represented as a vector from the 'origin' (0,0) to the point (a1,b1). If the second 'complex vector' (a2,b2) is added to the first, this can be shown as a translated vector with it's 'tail' starting at the arrowhead of the first vector, and then the arrowhead of the second vector will terminate at the sum of: a1 + ib1 + a2+ ib2 [coordinate point: (a1+a2,b1+b2)
Where was the complex number calculator invented?
It looks like at Bell Labs (part of the phone company) in 1940. It looks like it was in New York City, from the article in the related link.
How do you graph a complex number?
Take a number like 3+3i. It is a point at x=3 and y=3 and you can put that on graph
paper. With the proper software or program, you can graph more complex formulas
like (z-1)/(z+1). Look at the related link. It is one version of two like charges or two
like magnet poles near each other.
What are the sets of the real number negative 400?
They are all sets that contain it.
It belongs to {-400},
or {-400, sqrt(2), pi, -3/7},
or {-400, bananas, France, cold}
or all whole numbers between -500 and -300,
or multiples of 5,
or negative composite numbers,
or integers,
or rational numbers,
or real numbers,
or complex numbers,
etc.
Complex conjugate properties and their proofs?
The complex conjugate of x + yi, where x and y are real numbers, is x - yi.
(x + yi)*(x - yi) = x2 - xyi + xyi - y2i2 and since i2 = -1, the expression equals x2 + y2 which is real.
What are the applications of complex numbers?
- Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.
- Electricity, with AC, uses complex quantitites.
- Quantum physics
- Art - ever seen the Mandelbrot set, or other fractals?
There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include:
- Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.
- Electricity, with AC, uses complex quantitites.
- Quantum physics
- Art - ever seen the Mandelbrot set, or other fractals?
There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include:
- Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.
- Electricity, with AC, uses complex quantitites.
- Quantum physics
- Art - ever seen the Mandelbrot set, or other fractals?
There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include:
- Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.
- Electricity, with AC, uses complex quantitites.
- Quantum physics
- Art - ever seen the Mandelbrot set, or other fractals?
What is the difference between imaginary numbers and complex numbers?
No difference. The set of complex numbers includes the set of imaginary numbers.
You can determine by the discriminant whether the solutions to the equation are or complex numbers?
apex- real
Can a number be both complex and imaginary?
A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.
Is iota scalar quantity or vector quantity?
An iota is traditionally the smallest part imaginable, or even smaller, of whatever you may be thinking or talking about. And that may be anything, money, consideration, thought, courtesy, concentration of alcohol in beer, acceleration of a vehicle. The last is strictly a vector, although people generally think of its magnitude, which is a scalar. In general, if its a vector beihg talked about, the "iota" will be its magnitude, and so a scalar. Derived from the smallest Greek letter.
Why you pick 24 as lucky number?
Only because you are superstitious enough to believe that there is anything like a lucky number.
go into google and type things like "the natufians" or "natufian history" things like that and lots of things will come up about them! :) your welcome
What is the difference between principal argument and argument of a complex number?
PRINCIPAL ARGUMENT = ARGUMENT + 2nPI
arg(Z) = Arg (Z) + 2nPI
Does the set of numbers between 101 and 1000 include 101 and 1000?
No.
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Answer #2:
That depends on what you mean when you say "between". That's one of those
oily rubber words that can mean different things to different people, and so are
seldom used in real Science or real Math.
When some people say 'between', they intend to include 101 and 1,000,
while other people would intend NOT to include them.
In real Math, in order to avoid ambiguity, you would not say "between".
If you want to include the ends, you would write 101 ≤ N ≤ 1,000 and if you DON'T want to include the ends, then you write 101 < N < 1,000 .
A conjugate number refers to a complex number having both the imaginary and real parts of opposite signs and equal magnitude.
How is a complex number defined?
A complex number is a two-dimensional continuous quantity that is the sum of a real number and an imaginary number expressed in the form a+bi and plotted on a complex coordinate plane with the real line on the horizontal x-axis and the imaginary line on the vertical y-axis.
Is The product of a complex number and its conjugate is a real number.?
Yes. This is easy to prove; in the following, I'll use "^" for powers. Let the complex number be (a + bi), then its conjugate, by definition, is (a - bi). Multiplying them, you get a^2 + abi - abi + bi^2 = a^2 + bi^2 = a^2 - b^2 (since i^2 = -1).Update: One interesting, and quite useful, property is that the product of the complex number and its conjugate is equal to the square of the absolute value of the complex number.
When was eulers formula discovered?
Euler published the formula, which relates complex exponentials to trigonometric functions in 1748. See related link.
What the meaning of imaginary number with example?
An imaginary number is simply a number that contains 'i' which is simply shorthand for the square root of minus one. In the same way, we can write the square root of other negative numbers using i as a factor. For example;
Sqrt(-64) = Sqrt(-1*64) = Sqrt(-1)*Sqrt(64) = i*8 = 8i
There are also 'complex numbers' which are simply combinations of real numbers (all positive and negative numbers) and imaginary numbers. For example;
2+3i
Is a complex number. Although these numbers seem not to "exist" (it's impossible to have a set of 8i golf balls, or for you to weigh 3i kg) they are very useful in the fields of mathematics, physics, and engineering, and allowing their existence can save a lot of trouble when it comes to doing difficult math.
What is complex number of 10 12i?
You didn't say 10+12i or 10-12i
In the case of (10+12i), you would have a point in the xy plane @ x=10 and y=12
or (10,12)
In the case of (10-12i), you would have a point in the xy plane @ x=10 and y=-12
or (10,-12)
There are programs to "bend" photos with complex numbers.
Refer to the LINK and Source below.
Is addition of complex numbers commutative?
Yes, complex numbers obey the commutative property of addition.
