\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Given \(z_1 = e^{i\frac{2\pi}{3}}\) and \(z_2 = e^{i\frac{\pi}{3}}\), calculate and simplify the product \(z_1z_2\).
\(z_1z_2=\)