Part c
Analyze and determine the extrema of the real component of \(z(t)\) as \(t\) varies over \([0,2\pi]\).
Part b
Given the transformation matrix \( R = \begin{pmatrix}\cos 45^\circ & -\sin 45^\circ \\ \sin 45^\circ & \cos 45^\circ\end{pmatrix}\), apply it to the coordinates of a square’s vertex at \( (1, 0) \). Show your working to find the transformed coordinates.