\(i = e^{i \pi/2+2\pi k},~i \in \mathbb{Z}\\ z^2 = e^{i (\pi/2+2\pi k)}\\ z = \exp\left(i\dfrac{\frac \pi 2 + 2\pi k}{2}\right) =\\ \exp\left(i\left(\frac \pi 4 + \pi k\right)\right),~k = 0,1 = \\ e^{i\pi/4},~e^{i5\pi/4}=\\ \pm \dfrac{1}{\sqrt{2}}(1+i)\)
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