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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