cutiepiepolk cutiepiepolk

02-06-2017
Mathematics

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For z = 2cis 60°, find z4 in rectangular form.

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LammettHash LammettHash

02-06-2017

By DeMoivre's theorem,

[tex]z=2\mathrm{cis}60^\circ\implies z^4=2^4\mathrm{cis}(4\times60)^\circ=16\mathrm{cis}\,240^\circ[/tex]
[tex]z^4=16(\cos240^\circ+i\sin240^\circ)[/tex]
[tex]z^4=16\left(-\dfrac12-i\dfrac{\sqrt3}2\right)[/tex]
[tex]z^4=-8-i8\sqrt3[/tex]

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