Modulus and Argument of a Complex Number

Consider the complex number $z$ defined as follows:

$$ z = 3 - 4i $$

First, compute the modulus of the complex number $z$. The modulus of $z$ is given by the formula:

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

where $a$ is the real part and $b$ is the imaginary part of $z$. Here, $a = 3$ and $b = -4$.

Next, determine the argument of the complex number $z$. The argument, denoted as $ heta$, can be found using:

$$ heta = an^{-1}rac{b}{a} $$

Now, find the value of $|z|^2 + heta$ and enter your answer in the grid below.