A complex number is expressed in the form of $a + bi$, where $a$ and $b$ are real numbers and $i$ represents the imaginary unit defined by $i^2 = -1$. Consider the complex number $z = 3 + 4i$. The modulus of the complex number, denoted as $|z|$, is calculated using the formula:

$$|z| = ext{sqrt}(a^2 + b^2)$$

In this case, find the modulus $|z|$ of the complex number $z = 3 + 4i$. Round your answer to two decimal places.