Use DeMoivre’s Theorem to find the indicated power of the complex number .Write answer in rectangular form. (sqrt3-i)^6

midtlinjeg 2020-12-17 Answered
Use DeMoivre’s Theorem to find the indicated power of the complex number .Write answer in rectangular form.
(3i)6
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Expert Answer

comentezq
Answered 2020-12-18 Author has 106 answers
The complex number can be written as,
(3i)=2(32i12)
(3i)=2(cos(π6)+isin(π6))
therefore, it can be represented as,
2(cos(π6)+isin(π6))=2ei(π6)
therefore,
(3i)6=[2ei(π6)]6=26eiπ=64eπ
Therefore ,the given complex number can be simplified further as,
(3i)6=64(cos(π)+isin(π))=64(1)+i0)=64(1)=64
Hence, the given complex number becomes −64.
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