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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 are two complex numbers where neitjer a nor b are zero whose product is a real number?
Lets see............
(a+ib)(a-ib) = a^2+iab-iab+b^2
= a^2 + b^2
a and b can be any values and a^2+b^2 will be real.
What is the largest number of pieces you could cut a pie into with three straight cuts of a knife?
Eight. Use the first two cuts to cut the pie into four pieces, then use the third cut to slice the top from the bottom, doubling the number of pieces to 8.
I have many problems regarding complex numbers . will you solve them for me?
Those of us who love and eat complex numbers for lunch will HELP you to discover your hidden talents in solving your problems.
How can i convert real number to round that number?
An electron shell may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on further and further from the nucleus. The shell letters K, L, M, ... are alphabetical.
Each shell can contain only a fixed number of electrons: The 1 shell can hold up to two electrons, the 2 shell can hold up to eight electrons, and in general, the n shell can hold up to 2n2 electrons. Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: Atoms may have two or even three outer shells that are only partly filled with electrons. (See Madelung rule for more details.) For an explanation of why electrons exist in these shells see electron configuration.[1]
What is the domain of -1 to the x if you restrict the range to the real numbers?
(-1)^-2 = 1
(-1)^-1 = -1
(-1)^0 = 1
(-1)^1 = -1
(-1)^2 = 1
(-1)^3 = -1
For every whole number n (-1)^n equals either positive or negative 1.
How do you multiply a number containing a complex number?
One way, use binomial multiplication. Example: (w + x)*(y + z) = {using the FOIL method} w*y + w*z + x*y + x*z, so if we have two complex numbers multiplied:
(a + b*i)*(c + d*i) = a*c + a*d*i + b*c*i + b*d*i*i, but i*i = -1, so this becomes:
(a*c - b*d) + (a*d + b*c)*i
Another way to express complex numbers is as a magnitude and an angle. If this is the case, then you multiply the two magnitudes, and add the angles, then reduce the resultant angle to within -180° and +180°.
If you have a real X complex, then just use {b=0} in (a + b*i), so then you have:
(a*c) + (a*d)*i *Or if using the polar coordinates, take the angle as 0° for a positive real number and 180° for a negative real number, then add the angles.
How do you write 0.033579584 in words?
Thirty-three million, five hundred seventy-nine thousand, five hundred eighty-four billionths.
What is the result of the addition of two pure imaginary numbers?
An imaginary number.
Think of imaginary numbers as being on a vertical line while real numbers are on a horizontal line. (the lines cross at zero).
Adding and subtracting won't change the axis.
integers
What do you think is true of the square roots of a complex number?
I posted an answer about cube roots of complex numbers. The same info can be applied to square roots. (see related links)
Why is 3459 not an even number?
Because 3459 is not completely divisible by 2. Or 3459 is not multiple of 2.
What is the number for someone not wanting to give you there real number?
The answer depends on where real number!
Is a negative sign has a square root?
- Yes, a negative sign has a square root.
- This is done through using the imaginary unit defined as: i = .
- for example the square root of -36 is square root of (-1) multiplied by square root of 36. Accordingly it equals 6i
How the differences of the two squares relates to the product of a complex number and its conjugate?
In real number, when multiplying the difference of two squares, the middle term disappears:(a + b)*(a - b) = a^2 - ab + ab + b^2 = a^2 - b^2
Similarly, with the complex number and its conjugate, the imaginary term cancels out.
(a + ib)*(a - ib) = a^2 - iab + iab + (ib)^2 = a^2 - i^2b^2 = a^2 + b^2.
