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Question: The value of \({sinlog}\left( i^{i} \right)\) where \(i = \sqrt{- 1}\) is...

The value of sinlog(ii){sinlog}\left( i^{i} \right) where i=−1i = \sqrt{- 1} is

A

1

B

–1

C

0

D

None

Answer

–1

Explanation

Solution

Sol.log⁡eii=ilog⁡ei=ilog⁡eeiπ/2=i2π/2=−π/2\log_{e}i^{i} = i\log_{e}i = i\log_{e}e^{i\pi/2} = i^{2}\pi/2 = - \pi/2\sinlogeii=sin⁡(−π/2)=−1{sinlog}_{e}i^{i} = \sin( - \pi/2) = - 1