Applications of Complex Conjugates
When a real positive definite quantity is needed from a real function, the square of the function can be used. In the case of a complex function, the complex conjugateis used to accomplish that purpose. The product of a complex number and its complex conjugate is the complex number analog to squaring a real function. 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. Since the wavefunction which defines the probability amplitude may be a complex function, the probability is defined in terms of the complex conjugate to obtain a real value.
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