Part a
Rewrite \(z(t)= e^{it}+e^{-it}\) in terms of cosine and sine functions.
Part c
On the Argand plane, sketch the positions of the roots \(1, -1, i, -i\).
Part c
Evaluate \(z(t) = (1+t)\cos(t) + i(1+t)\sin(t)\) for the special parameter values \(t = \frac{\pi}{4}\), \(t = \frac{\pi}{2}\), and \(t = \pi\). Express your answers in Cartesian form and plot these points on an Argand diagram.

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