Complex Circle Locus in the Argand Diagram
Show that the locus of complex numbers satisfying \( |z – a| = r \) represents a circle in the Argand plane with center at the point corresponding to \(a\) and radius \(r\). Provide the Cartesian form of the circle equation.
Elimination of Parameter and Domain/Range Identification
Consider the parametric equations \(x = 2\cos(t)\) and \(y = 3\sin(t)\) for \(0 \leq t \leq 2\pi\). (a) Eliminate the parameter \(t\) to find the Cartesian equation relating \(x\) and \(y\). (b) Identify the domain and range of the resulting Cartesian equation.