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16-06-2017
Mathematics

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Which expression is the cube root of -1+i[tex] \sqrt{3} [/tex]

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LammettHash LammettHash

16-06-2017

[tex]z^3=-1+i\sqrt3=2e^{i2\pi/3}[/tex]

[tex]\implies z=\left(2e^{i2\pi/3}\right)^{1/3}=\begin{cases}2^{1/3}e^{i2\pi/9}\\2^{1/3}e^{i8pi/9}\\2^{1/3}e^{i14\pi/9}\end{cases}[/tex]

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