Let \(z = 3[\cos(85^{\circ})+i\sin(85^{\circ})]\). Find the smallest positive value of \(r\) such that \(r[\cos(45^{\circ})+i\sin(45^{\circ})] = z^n\) for some positive integer \(n\).
By DeMoivre's Theorem, the smallest possible value of r is 3^6 = 729.
