Consider the complex number $z = 3 + 4i$. The modulus of a complex number $z = x + yi$ is given by the formula:

$$|z| = ext{sqrt}(x^2 + y^2)$$

For the complex conjugate of $z$, denoted by $ar{z}$, the imaginary part is negated:

$$ar{z} = x - yi$$

Calculate the value of the expression $$z + ar{z} + |z|^2$$ and determine which of the following options provides the correct result.