Understand the difference between the argument, arg(𝑧), and the principal argument, Arg(𝑧) of a non-zero complex number 𝑧. arg(𝑧) = Arg(𝑧) + 2𝜋𝑛, 𝑛 ∈ ℤ

For the complex number \(z = -3 + 4i\): (a) determine the principal argument \(\operatorname{Arg}(z)\), correct to 2 decimal places; [1] (b) find an argument \(\operatorname{arg}(z)\) that lies in the range \((2\pi, 4\pi)\). [2]

Let z₁ = 2 + 2i and z₂ = -√3 - i. (a) Determine the principal argument Arg(z₁) and state one other value of arg(z₁) in the form Arg(z₁) + 2πn where n ∈ ℤ, n ≠ 0. (b) Determine all values of arg(z₂) that satisfy -2π < arg(z₂) ≤ 2π.

Given the complex number \(z = 3 + 3i\) has principal argument \(\text{Arg}(z) = \frac{\pi}{4}\), which of the following is the general argument \(\text{arg}(z)\) with \(n = 1\)?