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Question

If sin(loge ii) = A+iB where i = 1.Find the value of cos(loge ii).


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Solution

Given sin(loge ii) = A+iB

A+iB = sin(ilogei)

= sin [iloge(cosπ2+isinπ2)]

Express I in Euler's form

= sin [ilogeeiπ2]

= sin [i.iπ2]

= sin (π2) = -1

We know sin2θ + cos2θ = 1

sin2 (logeii) + cos2 (logeii) = 1

(1)2 + cos2 (logeii) = 1

cos2 (logeii) = 0

cos(logeii) = 0


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