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Chant6j

Chant6j

Answered question

2022-07-01

Resolve A = cos ( π / 7 ) + cos ( 3 π / 7 ) + cos ( 5 π / 7 ) using u = A + i B

Answer & Explanation

Asdrubali2r

Asdrubali2r

Beginner2022-07-02Added 14 answers

Using Euler formula,
setting 2 y = i π 7 e 14 y = 1
A + i B = r = 0 2 e ( 2 r + 1 ) 2 y = e 2 y 1 ( e 4 y ) 3 1 e 4 y = e 2 y + 1 1 e 4 y = 1 1 e 2 y
Now, 1 1 e i 2 u = e i u e i u e i u = cos u i sin u 2 i sin u = 1 2 + i cot u 2
Now equate the real parts.

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