Need help on trigonometry please
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Need help on trigonometry please

[From: ] [author: ] [Date: 11-12-11] [Hit: ]
-(√5 - 4i)=√21(cos -1.06105664796 + isin -1.(√5 - 4i)³=(√21)³(cos -1.06105664796 + isin -1.(√5 - 4i)³=(√21)³(cos -3.18316994389 + isin -3.......
Help using Demoivre's Theorem

Use Demoivre's Theorem to find (sqrt(5)-4i)^3. Write the result in Standard form.

r=sqrt(sqrt(5)^2+(-4)^2) = sqrt(5+16) = sqrt(21)

I am stuck after this step. I don't know what to do next or how I find theta.

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(√5 - 4i)=√21(cos -1.06105664796 + isin -1.06105664796)

(√5 - 4i)³=(√21)³(cos -1.06105664796 + isin -1.06105664796)³

(√5 - 4i)³=(√21)³(cos -3.18316994389 + isin -3.18316994389)

(√5 - 4i)³=(√21)³(cos -3.18316994389 + isin -3.18316994389)

(√5 - 4i)³=(√21)³(cos 3.10001536329 + isin 3.10001536329)

(√5 - 4i)³=96.2340895941(-0.999135788971+ i(0.041565312426)

(√5 - 4i)³=-96.1509230325+4i

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θ = tan^-1 (-4/√5) = -1.061 or -60.8°, approximately.

√21 (cos 1.061 - i sin 1.061) or √21 (cos 60.8° - i sin 60.8°)
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