You can not use the definition Hermitian inner product to solve this problem.
You need to use the definition of weight.
We need to generalize the equation.
1-Define the product, x*y , of two binary vectors of the same length to be the vector whose ith component is the product of the ith components of x and y.
Show that wt (x +y ) =wt (x ) +wt (y )- 2wt (x*y ).
See attached file for full problem description.