Modulus and Argument of a Complex Number

Consider the complex number $z = 3 - 4i$. Calculate the modulus of $z$ and express it in simplest radical form. Then, find the argument (angle) of $z$ in radians, and express your answer in the form of $a + b\pi$ where $a$ is a rational number and $b$ is an integer.

To find the modulus, use the formula: $$|z| = \sqrt{a^2 + b^2}$$ where $z = a + bi$. The argument can be derived using the formula: $$\theta = \tan^{-1}\left(\f\frac{b}{a}\right).$$