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

A value of θ for which z=2+3i sinθ12i sinθ is purely imaginary, is

A
π3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
π6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
sin1(34)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
sin1(13)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D sin1(13)
Let z=2+3i sinθ12i sinθ is purely imaginary. The, we have
Re(z) = 0
Now, consider z=2+3i sinθ12i sinθ
=(2+3i sinθ)(1+2i sinθ)(12i sinθ)(1+2i sinθ)=(2+4i sinθ+3i sinθ+6i2sin2θ)12(2i sinθ)2=(2+7i sinθ6sin2θ)1+4sin2θ=26sin2θ1+4sin2θ+i7sinθ1+4sin2θ
Re(z)=0
26sin2θ1+4sin2θ=02=6sin2θ
sin2θ=13sinθ=±13θ=sin1(±13)=±sin1(13)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Representation and Trigonometric Form
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon