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

Let z be an imaginary complex number satisfying |z1|=1. If α=2z, β=2α and γ=2β, then the value of |z|2+|α|2+|β|2+|γ|2+|z2|2+|α4|2+|β8|2+|γ16|2 is

A
100
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
320
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
340
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
400
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 340

As we can see,
|z|2+|z2|2=4 (1)
Similarly,
|α|2+|α4|2=16 (2)
|β|2+|β8|2=64 (3)
|γ|2+|γ16|2=256 (4)

Adding all the above equations (1),(2),(3) and (4),
|z|2+|α|2+|β|2+|γ|2+|z2|2+|α4|2+|β8|2+|γ16|2=340

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