Complex number in cosine: cos &#x2061;<!-- ⁡ --> ( log &#x2061;<!-- ⁡ --> (

Brice Colon

Brice Colon

Answered question

2022-05-22

Complex number in cosine: cos ( log ( i 4 i ) )

Answer & Explanation

Lavizzariym

Lavizzariym

Beginner2022-05-23Added 10 answers

k Z : e i ( π / 2 + 2 k π ) = i ln i = { i π 2 + 2 k i π : k Z } 4 i ln i = { 2 π 8 k π : k Z } exp ( 4 i ln i ) = { exp ( 2 π 8 k π ) : k Z } i 4 i = { exp ( 2 π 8 k π ) : k Z } ln ( i 4 i ) = { 2 π 8 k π + 2 n i π : k , n Z } cos ln ( i 4 i ) = { cos ( 2 n i π ) : n Z } = { exp ( 2 n i π ) + exp ( 2 n i π ) 2 : n Z } = { 1 + 1 2 : n Z } = 1

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