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lf z = ilog(2-sqrt(-3)), then cos z =...

lf `z = ilog(2-sqrt(-3))`, then `cos z =`

A

`-1`

B

`-1//2`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
`z=ilog(2=sqrt3)`
`rArr e^(iz)=e^(i"^(2)log(2-sqrt3))=e^(-log(2-sqrt3))`
`=e^(log(2-sqrt3)^(-1))=e^(log(2+sqrt3))=(2+sqrt3)`
`rArr cosz=(e^(iz)+e^(-iz))/(2)=((2+sqrt3)+(2-sqrt3))/(2)=2`
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