A number multiplied by its complex conjugate will result in a real number. Also, adding a number to its conjugate will result in a real number. But typically the multiplication is what is used.
With math for most people, the set of complex numbers can be considered to enclose all other sets of numbers.There are, however, sets of numbers that have been created which are outside the scope of 'complex numbers'.
Mainly engineering, particularly control theory and other electronic systems; complex numbers are useful to represent oscillation frequency and phase information.
Always. The set of imaginary numbers is a subset of complex numbers. Think of complex numbers as a plane (2 dimensional). The real numbers exist on the horizontal axis. The pure imaginary are the vertical axis. All other points on the plane are combinations of real and imaginary. All points on the plane (including imaginary axis and real axis) are complex numbers.
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 physicsArt - 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 physicsArt - 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 physicsArt - 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 physicsArt - ever seen the Mandelbrot set, or other fractals?
Real and Complex. Real numbers are your everyday numbers that most people are familiar with and Complex numbers are Real numbers mixed with imaginary numbers. Of course this is a VERY BROAD oversimplification, and the question is somewhat vague in that there are other "types" of numbers that are used, but I think this is the answer you are looking for.
One part is that the RE part and the IM part are at right angles to each other. Refer to the related link for a picture of an array of complex numbers. Notice the curves are at right angles to each other.
Non-Zero Real Numbers are infact complex conjugate numbers. They are negative prime numbers.
The conjugate of a complex number is the same number (but the imaginary part has opposite sign). e.g.: A=[5i - 2] --> A*=[-5i - 2] Graphically, as you change the sign, you also change the direction of that vector. The conjugate it's used to solve operations with complex numbers. When a complex number is multiplied by its conjugate, the product is a real number. e.g.: 5/(2-i) --> then you multiply and divide by the complex conjugate (2+i) and get the following: 5(2+i)/(2-i)(2+i)=(10+5i)/5=2+i
The 16th century Italian mathematician, Gerolamo Cardano was the first to use imaginary and complex numbers in his work on cubic equations.
It need not be. For example, a complex number as a percent of most other complex numbers, or any real number, will not be a real number.
All integers are also whole numbers that are rational
The properties of an array or group or complex numbers form a system of real and imanginary numbers that are at a 90 degree angle to each other. Refer to the Related Link and notice that in both panes, the lines are at 90 degrees.