Question

The multi-valued function arg z can be visualized by following the below steps: (a) Write the complex number z in polar form. What are x =Re z and y =Im z in terms of r and θ? (b) Plot the surface x = x(r, θ), y = y(r, θ), w = θ using the command ParametricPlot3D. (For better visualization, choose the range of θ to be wide, for example from 0 to 10π, and the range of r to be relatively wider than 2π, for example from 0 to 10.)

make sure to write the Mathematica code you use, give explanation and some comments on the graph.

Answer 1

a) When we write a complex number z in polar form, it looks like y= Im z= r sin θ The given function is w arg z = θ b) to generate surface ParametricPlot3DI (yw. .Tmin Tmaxt, tmin where t stands for θ, has to be used. max) y-y(r, θ) r sin θ And w θ ParametricPlot3DIfr cos t, r sin t,t), fr, 1min, Timax), st, tmin, tmaxl