Solve cos &#x2061;<!-- ⁡ --> ( z ) + sin &#x2061;<!-- ⁡ --> ( z )

Monfredo0n

Monfredo0n

Answered question

2022-05-21

Solve cos ( z ) + sin ( z ) = 2
My work:
cos ( z ) + sin ( z ) = 2 e i z + e i z + e i z e i z = 4 e i z = 2 e i z = e ln ( 2 ) + 2 π n i i z = ln ( 2 ) + 2 π n i z = i ln ( 2 ) 2 π n
but apparently the answer is z = π 4 + 2 n π ± i ln ( 2 + 1 )

Answer & Explanation

Leah Conley

Leah Conley

Beginner2022-05-22Added 12 answers

Hint:
cos ( z ) = e i z + e i z 2
sin ( z ) = e i z e i z 2 i

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