Complex Numbers & Complex Envelopes: Articles & Resources

In summary, complex numbers are numbers that have a real part and an imaginary part, represented as a + bi. They are used to represent quantities with both real and imaginary values, and are commonly used in fields such as physics, engineering, and mathematics. Complex envelopes, which represent complex signals as a combination of a real envelope and a complex carrier, are closely related to complex numbers. Complex numbers are widely used in real-world applications such as electronic circuits, signal processing, and control systems. There are rules for operating with complex numbers, which take into account both the real and imaginary components.
  • #1
dervast
133
1
Hi i need some good articles about complex number and more especially with complex envelopes...Do u have anything in mind? Thx a lot
 
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  • #2
I don't know which level you need, but here is a very basic tutorial on complex numbers:

http://tutorial.math.lamar.edu/AllBrowsers/Complex/ComplexNumbers.asp
 
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  • #3
here is something I was reading the other day :

www.maths.bris.ac.uk/~maxmg/maths/introductory/complex.html[/URL]
 
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1) What are complex numbers and how are they represented?

Complex numbers are numbers that consist of a real part and an imaginary part. They are represented in the form a + bi, where a is the real part and bi is the imaginary part with i being the square root of -1.

2) What is the purpose of using complex numbers?

Complex numbers are used to represent quantities that involve both real and imaginary values. They are especially useful in fields such as physics, engineering, and mathematics where calculations involving imaginary numbers are common.

3) What is a complex envelope and how is it related to complex numbers?

A complex envelope is a mathematical concept that is used to represent a complex signal as a combination of two simpler signals, a real envelope and a complex carrier. This concept is closely related to complex numbers as the imaginary part of a complex number represents the complex carrier in a complex envelope.

4) Can complex numbers be used in real-world applications?

Yes, complex numbers are widely used in various real-world applications such as electronic circuits, signal processing, and control systems. They are also essential in the study of electromagnetic fields and waves.

5) Are there any rules for operating with complex numbers?

Yes, there are rules for performing operations such as addition, subtraction, multiplication, and division with complex numbers. These rules are similar to the rules for operating with real numbers, but they also take into account the imaginary component of complex numbers.

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