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Find all solutions of the equation. leave answers in trigonometric form x^3-8=0 2cis
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Find all solutions of the equation. leave answers in trigonometric form x^3-8=0 2cis

User Dhythhsba
by
9.1k points

1 Answer

2 votes


x^3-8=0


x^3=8=8\mathrm{cis}\,0^\circ

By DeMoivre's theorem, we have


x=8^(1/3)\mathrm{cis}\left(\frac{0^\circ+360^\circ k}3\right)

with
k=0,1,2. Then we have three solutions,


x=2\mathrm{cis}\,0^\circ=2


x=2\mathrm{cis}\,120^\circ


x=2\mathrm{cis}\,240^\circ

User Nicolas Pepinster
by
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