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Question: Answered & Verified by Expert
1+cos(3θ)+isin(3θ)1+cos(3θ)-isin(3θ)20=?
MathematicsComplex NumberAP EAMCETAP EAMCET 2020 (23 Sep Shift 1)
Options:
  • A cos(60θ)+isin(60θ)
  • B cos(60θ)-isin(60θ)
  • C cos(20θ)+isin(20θ)
  • D cos(20θ)-isin(20θ)
Solution:
1093 Upvotes Verified Answer
The correct answer is: cos(60θ)+isin(60θ)

1+cos3θ+ i sin3θ1+cos3θ-i sin3θ20

=2cos23θ2+i2sin 3θ2·cos3θ22cos23θ2-i2sin3θ2·cos3θ220

=cos3θ2+i sin3θ2cos3θ2- isin3θ220

=ei3θ2e-i3θ220

=(ei3θ)20

=(ei60θ)

=cos(60θ)+i sin(60θ)

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