$\begin{aligned} & \text { Given, } z_r=\cos \left(\frac{\pi}{2^{\prime}}\right)+i \sin \left(\frac{\pi}{2^r}\right) \\ & \therefore z_1 z_2 z_3 \ldots=e^{i \frac{\pi}{2}} \cdot e^{i \frac{\pi}{2^2}} \cdot e^{i \frac{\pi}{2^3}} \ldots \\ & =e^{i\left(\frac{\pi}{2}+\frac{\pi}{2^2}+\frac{\pi}{2^3}+\ldots\right)} \\ & =e^{i\left(\frac{\pi / 2}{1}\right)}=e^{\lambda(\pi)} \\ & =\cos \pi+i \sin \pi=-1+i(0) \\ & =-1 \\ & \end{aligned}$