CV14

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List all the cube roots of -1+i\,.

\theta = \tan^{-1}\frac{y}{x} = \tan^{-1}(-1) = \frac{3\pi}{4}\,

r = \sqrt{2}\,

-1+i = \sqrt{2}\exp(i\frac{3\pi}{4}+2k\pi), k=0,1,2\,

(-1+i)^{1/3} = 2^{1/6}\exp\frac{i}{3}\left(\frac{3\pi}{4}+2k\pi\right), k=0,1,2\,

(-1+i)^{1/3} = 2^{1/6}e^{i\frac{\pi}{4}}, 2^{1/6}e^{i\frac{11\pi}{12}}, 2^{1/6}e^{i\frac{19\pi}{12}}\,

Complex Variables

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