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

Let z1 and z2 be any two non-zero complex numbers such that 3|z1|=4|z2|. If z=3z12z2+2z23z1 then :

A
Im(z)=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Re(z)=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
|z|=12172
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
|z|=52
No worries! We‘ve got your back. Try BYJU‘S free classes today!
E
Re(z)=52cos(θ1θ2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is E Re(z)=52cos(θ1θ2)
z1=r1eiθ1, z2=r2eiθ2
z1z2=r1eiθ1r2eiθ2=r1r2ei(θ1θ2)
Since, 3|z1|=4|z2|
3r1=4r2r1r2=43
z1z2=43ei(θ1θ2)
Similarly,
z2z1=34ei(θ2θ1)
Now,
z=3z12z2+2z23z1 =32×43ei(θ1θ2)+23×34ei(θ2θ1)
z=2cos(θ1θ2)+2isin(θ1θ2) +12cos(θ2θ1)+12isin(θ2θ1)

z=52cos(θ1θ2)+32isin(θ1θ2)

|z|=254cos2(θ1θ2)+94sin2(θ1θ2)
Im(z)=32sin(θ1θ2)
Re(z)=52cos(θ1θ2)

No options matches with the answer,
It is bonus question.

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