



 
Hi Deepak, $\large \frac{1}{2^i}$ can be written $2^{i}$ and Euler's formula says that for a real number $\theta$ \[e^{i \theta} =cos \theta + i \sin \theta\] so you can simplify \[z = \frac{1}{2^i}\] if you can write $z$ in the form $e^{i \theta}.$ Since $z = 2^{i}$ you can take the natural logarithm of each side to get \[log(z) = \log\left(2^{i}\right) = i \log(2)\] and applying the exponential function to each side to get \[z = e^{i \log(2)} = e^{i[\log(2)]}.\] Penny
 


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