z^2=6\,\text{cis}\left(\dfrac{2\pi}{3}\right)

z^2=9\,\text{cis}\left(\dfrac{\pi}{3}\right)

z^2=9\,\text{cis}\left(\dfrac{\pi}{12}\right)

z^2=6\,\text{cis}\left(\dfrac{\pi}{3}\right)

r=3 and \theta = \pi hence 

z=3\,\text{cis}\left(\pi\right)=3e^{\pi i}.

r=-3 and \theta = \pi hence 

z=-3\,\text{cis}\left(\pi\right)=-3e^{\pi i}.

r=\sqrt{3} and \theta = \pi hence 

z=\sqrt{3}\,\text{cis}\left(\pi\right)=\sqrt{3}e^{\pi i}.

r=3 and \theta = -\dfrac{\pi}{2} hence 

z=3\,\text{cis}\left(-\dfrac{\pi}{2}\right)=3e^{-\frac{\pi}{2}i}.

r=4 and \theta = \dfrac{\pi}{2} hence 

z=4\text{cis}\left(\dfrac{\pi}{2}\right)=4e^{\frac{\pi}{2}i}.

r=2 and \theta = \pi hence 

z=2\text{cis}\left(\pi\right)=2e^{\pi i}.

r=2 and \theta = \dfrac{\pi}{2} hence 

z=2\text{cis}\left(\dfrac{\pi}{2}\right)=2e^{\frac{\pi}{2}i}.

r=\sqrt{2} and \theta = \dfrac{\pi}{2} hence 

z=\sqrt{2}\text{cis}\left(\dfrac{\pi}{2}\right)=\sqrt{2}e^{\frac{\pi}{2}i}.

r=-\sqrt{2} and \theta = \dfrac{3\pi}{4} hence 

z=-\sqrt{2}\text{cis}\left(\dfrac{3\pi}{4}\right)=-\sqrt{2}e^{\frac{3\pi}{4}i}.

r=\sqrt{2} and \theta = -\dfrac{\pi}{4} hence 

z=\sqrt{2}\text{cis}\left(-\dfrac{\pi}{4}\right)=\sqrt{2}e^{-\frac{\pi}{4}i}.

r=\sqrt{2} and \theta = \dfrac{3\pi}{4} hence 

z=\sqrt{2}\text{cis}\left(\dfrac{3\pi}{4}\right)=\sqrt{2}e^{\frac{3\pi}{4}i}.

r=2 and \theta = \dfrac{3\pi}{4} hence 

z=2\text{cis}\left(\dfrac{3\pi}{4}\right)=2e^{\frac{3\pi}{4}i}.

r=2 and \theta = \dfrac{\pi}{4} hence 

z=2\text{cis}\left(\dfrac{\pi}{4}\right)=2e^{\frac{\pi}{4}i}.

r=1 and \theta = \dfrac{\pi}{4} hence 

z=\text{cis}\left(\dfrac{\pi}{4}\right)=e^{\frac{\pi}{4}i}.

r=\sqrt{2} and \theta = \dfrac{\pi}{4} hence 

z=\sqrt{2}\text{cis}\left(\dfrac{\pi}{4}\right)=\sqrt{2}e^{\frac{\pi}{4}i}.

r=\sqrt{2} and \theta = \dfrac{3\pi}{4} hence 

z=\sqrt{2}\text{cis}\left(\dfrac{3\pi}{4}\right)=\sqrt{2}e^{\frac{3\pi}{4}i}.

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