\(z^5 = 1\\ z = \Large e^{i 2\pi \frac{k}{5}}, \normalsize k=0,1,\dots 4\)
\(\text{It might be a bit easier to visualize the quadrants if we write these as degrees}\\ r = (0, 72, 144, 216, 288)^\circ\\ \text{and clearly }180 < 216 < 270\\ 216^\circ \Rightarrow e^{i 2\pi \frac 3 5}\\ r = 1,~\theta = \dfrac{6\pi}{5}\)
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