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Question

Find the value of i.ii is _______.


A

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B

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C

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D

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Solution

The correct option is B


Let z = i.ii

Taking log on both sides

logez = logei + log0ii

= loge(cosπ2+isinπ2)+iloge(cosπ2+isinπ2)

= logeeiπ2+ilogeeiπ2

= iπ2 + i.iπ2

loge2 = iπ2 - π2 = π2(i-1)

z = e(π2+iπ2)

= eπ2.eiπ2

= eπ2.(cosπ2+isinπ2)

= eπ2 (i)

= i.eπ2


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