Does it make sense to have complex numbers representing real-world audio signals?

1. How complex numbers are useful in real world applications?
2. Why do we use complex numbers for signals?
3. Do imaginary numbers have used in the real world?
4. How is complex signal different from real signal?

How complex numbers are useful in real world applications?

Complex numbers are also used to understand our technological devices because they make up the language of alternating current (AC) electronics. Using imaginary currents, together with real numbers, helps the people who are working with AC electricity, do the calculations while avoiding electrocution.

Why do we use complex numbers for signals?

They have the unique property of representing and manipulating two variables as a single quantity. This fits very naturally with Fourier analysis, where the frequency domain is composed of two signals, the real and the imaginary parts.

Do imaginary numbers have used in the real world?

Imaginary numbers, also called complex numbers, are used in real-life applications, such as electricity, as well as quadratic equations. In quadratic planes, imaginary numbers show up in equations that don't touch the x axis. Imaginary numbers become particularly useful in advanced calculus.

How is complex signal different from real signal?

A real signal at any given time takes its value in the set of real numbers, and a complex signal takes its value in the set of complex numbers.