Value of z in sin &#x2061;<!-- ⁡ --> z = 1 2 </mfrac> <msqrt> 2 </msqr

Chaz Blair

Chaz Blair

Answered question

2022-05-29

Value of z in sin z = 1 2 2 ( 1 i )?
I have tried with the equation sin z = e i z e i z 2 i = 1 2 2 ( 1 i ) but I get stuck and can't make it simpler. Is there possible to make the value much simpler?

Answer & Explanation

vrhnjemuvs

vrhnjemuvs

Beginner2022-05-30Added 4 answers

e i z e i z = 2 i sin z = 2 ( 1 + i )
Now 1 + i = 2 e i π / 4
On rearrangement,
( e i z ) 2 2 e i π / 4 e i z 1 = 0
e i z = 2 e i π / 4 ± ( 2 e i π / 4 ) 2 + 4 2
e i ( z π / 4 ) = 1 ± e i π / 4 + e i π / 4
Now e i π / 4 + e i π / 4 = 2 cos π 4 = 2

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