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gvaldytist

gvaldytist

Answered question

2022-06-07

If ( 1 + cis x ) ( 1 + cis 2 x ) = a + b i, prove that a 2 + b 2 = ( 4 cos x cos x 2 ) 2

Answer & Explanation

Eleanor Luna

Eleanor Luna

Beginner2022-06-08Added 19 answers

Note
a 2 + b 2 = | a + b i | 2 = | ( 1 + cis x ) ( 1 + cis 2 x ) | 2 = | 1 + e i x | 2 | 1 + e i 2 x | 2 = | e x 2 + e x 2 | 2 | e i x + e i x | 2 = | 2 cos x 2 | 2 | 2 cos x | 2 = ( 4 cos x cos x 2 ) 2

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