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

If tan(α+iβ)=eiθ ; where α,βR, θ(2n+1)π2,nZ and i=1, then

A
α is an odd multiple of π2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
α is an even multiple of π2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
α is an odd multiple of π4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
α is an even multiple of π4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C α is an odd multiple of π4
tan(α+iβ)=eiθ
tan(α+iβ)=cosθ+isinθ
Taking complex conjugate, we get
tan(αiβ)=cosθisinθ

tan2α=tan[(α+iβ)+(αiβ)]

tan2α=tan(α+iβ)+tan(αiβ)1tan(α+iβ)tan(αiβ)

1tan2α=1tan(α+iβ)tan(αiβ)tan(α+iβ)+tan(αiβ)

cot2α=1(cos2θ+sin2θ)2cosθ

cot2α=0 [θ(2n+1)π2]

2α=(2m+1)π2,mZ

α=(2m+1)π4,mZ

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon