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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
What is the phone number of the National Orphan Train Complex in Concordia Kansas?
The phone number of the National Orphan Train Complex is: 785-243-4471.
What the advantges of complex numbers?
one advantage is that it is easy to graph some electrical situations like the magnetic
fields around two conductors carrying current. the complex formula is w=(z-1)/(z+1).
notice the fields are at right angles to each other. REFER TO THE LINK FOR A PICTURE.
Define a complex number using c structure?
Just define two fields (whatever those are called in "C" - the parts of the structure), one for the real part, one for the imaginary part.
Just define two fields (whatever those are called in "C" - the parts of the structure), one for the real part, one for the imaginary part.
Just define two fields (whatever those are called in "C" - the parts of the structure), one for the real part, one for the imaginary part.
Just define two fields (whatever those are called in "C" - the parts of the structure), one for the real part, one for the imaginary part.
Why is the square root of a negative number imaginary?
Any real number, when squared will give a positive real number. This is true weather you have a negative real number and square it, or positive. The concept of imaginary numbers was invented to handle equations which needed to use the square root of a negative number, in order to solve them.
At first, they were not considered useful beyond this, so they were named imaginary numbers. Through the work of Euler and others, it became evident that imaginary and complex numbers could be useful, especially when analyzing waves, such as electrical waveforms.
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
What are Complex and imaginary numbers?
A complex number is like x+iy = 3+i6 and "i" is the imaginary unit.
A formula like w=(z^3-1)/(z^3-i) when graphed, makes interesting art. See the
below link for a picture.
Why imaginary numbers are used?
Originally, they were invented to provide solutions to algebraic equations, which would otherwise have no solution. Through the work of Euler, Gauss and others, the usefulness of imaginary and complex numbers in applications of periodic motion and waves was recognized. See related links.
What is the correct form in which to express complex numbers?
Actually there are several methods.
- The most commonly used method is in rectangular coordinates, that is, specifying the real and the imaginary part separately.
- This is usually written as a + bi, where a and b are real numbers; for example: 5 + 3i, or 3 - 2i.
- In electricity, "i" is a symbol for instantaneous current; so, to avoid confusion, the symbol "j" is used instead. Also, it is considered an operator, and written in front of the imaginary part. Examples; 5 + j3, or 3 - j2.
- Multiplication, division, and especially exponentiation and radication, are simpler when the complex number is in polar coordinates. That is, an absolute value and an angle.
- This might be written, for example, as 5 (angle symbol) 30 degrees, as is common in electricity.
- In pure math, the equivalent exponential notation is used instead; and the angle is expressed in radians: reia, where r is the absolute value, and a is the angle (often some Greek letter is used for the angle, such as thetha, or phi).
Where did the imaginary number symbol i come from?
"i" stands for imaginary. It represents the square root of -1.
What does putting quotations after a number mean?
Inches. (i.e. 6" means six inches, whereas 6' means 6 feet)
How can you tell which part of a complex number is the real part and which is the imaginary part?
The imaginary part is expressed as a product of i(square root of negative one), typically following a plus sign, so that the complex number has the form a + bi, with "a" the real part and "bi" the imaginary part.
There are many reasons, but the one I'm fond of is that if you plot a complex equation, you can visualize certain aspects of say electricity. A plot of w=(z-1)/(z+1)
can show a possible electromagnetic field of two wires carrying current as depicted
in the below LINK.
How do you write complex numbers in the form a plus bi?
A complex number comes in two parts: a real part and an imaginary part. If the value of the real part is a and the value of the imaginary part is b, the number is written as a + bi.
What are set of complex number?
Complex numbers are numbers of the form (x + yi) where x and y are real numbers and i is the imaginary square root of -1.
Any collection of such numbers is a set of complex numbers.
Is RR subset of complex number C?
If a complex number z = (x, y) = x +iy where x and y are real numbers (and i is the imaginary root of -1), then RxR is is isomorphic to C. This means that the two sets are equivalent.
What imaginary number is equivalent to the square root of negative 64?
8i and -8i both satisfy this: (8i)² = (8²)(i²) = (64)(-1) = -64, and
(-8i)² = (-8²)(i²) = (64)(-1) = -64
Is the difference of a complex number and its conjugate a real imaginary or pure imaginary number?
It is a pure imaginary number.
Since (a+bi)-(a-bi) = 2bi, it is a pure imaginary number (it has no real component).
