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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
If you put it into matrix form, A*x = p. With A a square matrix, and x & p are column matrices, then you can separate matrix A becoming B + Ci where B contains the real parts of the coefficients, and C contains the imaginary components, then p = m + ni, and x = y + zi, then the real parts must be equal, and the imaginary parts must be equal, so:
B*y = m, and C*z = n, solve each set of equations for y & z, then your solution set will be x = y + zi.
A complex number, equations and graphs can show electromagnetic forces-for instance two wires carrying current. A formula like (z-1)/(z+1) can show the fields around two parallel wires.
What are Real and Complex numbers?
Real numbers are numbers that you are already familiar with: integers, fractions, and irrational numbers: 1, 2, 0, -5, ¾, sqrt(2), pi, etc. Next, you need to know about imaginary numbers. These are numbers that, when squared, will give a negative real number. No real number can do that. Now imagine a graphical plane, with the real axis on the horizontal, and the imaginary axis on the vertical. This is called the complex plane, and any combination of real and imaginary numbers can be plotted on the complex plane.
The set of complex numbers includes all real numbers as well as all imaginary numbers, and the combination of the two.
Why is it advantageous for a circuit designer to use the least number of chips possible?
To minimize the size.
What are the propenties of real numbers?
A number that is "real". In other words, it actually exists. As apposed to "imaginary" numbers. Which really is only one. The square root of a negative one.
Who work on function of complex numbers in geometry?
Caspar Wessel, a Norwegian and Danish mathematician was the first to porpose representing complex numbers in a two dimensional plane using real and imaginary axes. The idea was developed by Jean-Robert Argand, a Frenchman.
A real number is not a question nor an equation or inequality that can be solved. There may be questions associated with real numbers that may be solved but that is not the same as solving the real number. The question is like asking how someone can solve you!
x = √(2-x)
x2 = 2-x
x2 + x = 2
x2 + x - 2 = 0
(x+2)(x-1) = 0
x = 1 or -2
it's Barclays (apparently) trying to sell Personal Accident Cover insurance.
What is the relationship between number of set and number of elements?
There may not be any relationship between number of sets and number of elements. You can have just one set or thousands of sets. Similarly, you can also have just one element (rare) or thousands of elements.
Probably because if you consider real numbers, you are not interested in complex numbers.Any complex number other than zero - and that includes real numbers - has three cubic roots, which have an angle of 120 degrees between one another. For example, the cubic roots of 1 are 1, 1 at an angle of 120°, and 1 at an angle of 240°. Similarly, the cubic roots of -1 are 1 at an angle of 180° (equal to -1), 1 at an angle of 60°, and 1 at an angle of 300°.
Rafael Bombelli is usually credited with discovering imaginary numbers in 1572.
There were hints of the theory going back much further, perhaps beginning with Hero of Alexandria in the first century.
What are the sets of numbers that are part of the complex number system?
Real number set, imaginary number set, and their subsets.
What is a complex combination of pure topologies?
The complex combination of pure topologies is called a Hybrid. Examples of hybrid are star ring network and star bus network.
It is the arithmetic average or mean.
Name 2 complex number that when multiplied together become a real number?
Any pair of complex conjugates do that.
No, both positive and negative numbers are part of the so-called "real" numbers. The so-called "imaginary" numbers are outside the number line.
Imagine the real numbers as a line from left to right, and the imaginary numbers a a separate line, from top to bottom. The place where they meet is zero. Positive is to the right of zero, negative to the left, imaginary numbers like +i or +3i to the top of zero, and negative imaginary numbes like -5i to the bottom of zero.
