Howtosignalprocessing
- What is the complex conjugate used for?
- Do complex conjugates cancel out?
- What happens when you multiply complex conjugates together?
- What happens when you add complex conjugates?
What is the complex conjugate used for?
The complex conjugate is used in the rationalization of complex numbers and for finding the amplitude of the polar form of a complex number. One application of the complex conjugate in physics is in finding the probability in quantum mechanics.
Do complex conjugates cancel out?
Well, the same thing happens here when you multiply the complex number in the denominator by its complex conjugate: the imaginary number middle terms will cancel each other out!
What happens when you multiply complex conjugates together?
The complex conjugate has a very special property. Consider what happens when we multiply a complex number by its complex conjugate. We find that the answer is a purely real number - it has no imaginary part. This always happens when a complex number is multiplied by its conjugate - the result is real number.
What happens when you add complex conjugates?
The sum of a complex number and its conjugate will always be two times the real part of that complex number.
