wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the value of i.ii is _______.


A

i.eπ2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

i.eπ2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

i.eπ4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

i.eπ4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

i.eπ2


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


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Logarithm of a Complex Number
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon