Let z₀ be a complex number with polar coordinates (r₀, θ₀) and Cartesian coordinates x₀, y₀. Determine expression for the Cartesian coordinates of the following complex numbers in terms of x₀ and y₀. Plot the points z₀, z₁, z₂, z₃, z₄, and z₅ in the complex plane when r₀ = 2, θ₀ = π/4 and when r₀ = 2 and θ₀ = π/2. Indicate on your plots the real and imaginary parts of each point.
a) z₁ = r₀e⁻ʲθ₀
b) z₂ = r₀
c) z₃ = r₀eʲ⁽θ₀ ⁺ ʷ⁾
d) z₄ = r₀eʲ⁽⁻⁽θ₀ ⁺ ʷ⁾
e) z₅ = r₀eʲ⁽θ₀ ⁺ ²ʷ⁾