Frequencies in frequency spectrum with no correlation together

1. What are negative frequencies in spectrum?
2. Is it possible to have negative frequency?
3. What does a frequency spectrum tell you?
4. Why we have negative frequencies needed in the spectrum?

What are negative frequencies in spectrum?

Negative frequency is an idea associated with complex exponentials. A single sine wave can be broken down into two complex exponentials ('spinning numbers'), one with a positive exponent and one with a negative exponent. That one with the negative exponent is where you get the concept of a negative frequency.

Is it possible to have negative frequency?

The meaning of negative frequencies is just mathematical(not physical) similarly to the imaginary part of a complex signal. In real world, the negative frequency does not exists and the spectral content on negative frequencies must be added to the spectral content at the positive frequencies, to save energy.

What does a frequency spectrum tell you?

Frequency spectrum of a signal is the range of frequencies contained by a signal.

Why we have negative frequencies needed in the spectrum?

Negative frequencies are just a mathematical construct to allow us to analyse real signals using a complex number framework, which is used when looking at double-sided spectra. A complex number can only be made real if you add to it its conjugate, e.g. (a+bj) + (a-bj) = 2a.