For each value of \(\mu\) and \(\sigma\) listed below, plot the characteristic function of the corresponding \(\mathrm{N}\left(\mu, \sigma^{2}ight)\) distribution as a function of \(t\) in the complex plane. Describe how the changes in the parameter values affect the properties of the corresponding characteristic function. This will require a three-dimensional plot.

a. \(\mu=0, \sigma=1\)

b. \(\mu=1, \sigma=1\)

c. \(\mu=0, \sigma=2\)

d. \(\mu=1, \sigma=2\)