For Quantum Mechanics suppose a complex number is such that

For Quantum Mechanics, suppose a complex number is such that its real component is cos(x) for any value of x, and its imaginary component is sin(x). Does the square magnitude of this complex number depend on x? Explain why you answered Yes or No.

Solution

Yes it depends on the value of x.

because the squared magnitude of this complex number gives the probability of finding the particle at a particular position. for example suppose we have a number Y= 1+i, here x=1, so the probability of finding at x=1 is [1+i]² =2.