Asked by JJ
Evaluate (5+5√3i)^7 using DeMoivre’s theorem.
Write your answer in rectangular form. Show all your work.
Write your answer in rectangular form. Show all your work.
Answers
Answered by
Reiny
let z = 5+5√3i = 5(1 + √3i)
magnitude = 5√(1+3) = 10
tanØ = 5/√3/5 = √3
Ø = 60°
z = 10(cos60° + i sin60°)
z^7 = 10^7(cos420° + i sin 420°)
= 10^7(cos60 + isin 60) , since cos 420 = cos(360+60) = cos60 , same for sin420
= 10^7/2 + i√3 10^7/2
magnitude = 5√(1+3) = 10
tanØ = 5/√3/5 = √3
Ø = 60°
z = 10(cos60° + i sin60°)
z^7 = 10^7(cos420° + i sin 420°)
= 10^7(cos60 + isin 60) , since cos 420 = cos(360+60) = cos60 , same for sin420
= 10^7/2 + i√3 10^7/2
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