wiz-icon
MyQuestionIcon
MyQuestionIcon
12
You visited us 12 times! Enjoying our articles? Unlock Full Access!
Question

If α and β are different complex numbers with |β|=1, then the value of βα1¯¯¯¯αβ is

A
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 1
Given, |β|=1|β|2=1
β¯¯¯β=1
β=1¯¯¯β (1)

Now, βα1¯¯¯¯αβ=∣ ∣ ∣ ∣ ∣1¯¯¯βα1¯¯¯¯αβ∣ ∣ ∣ ∣ ∣
=|β|∣ ∣1α¯¯¯β1¯¯¯¯αβ∣ ∣ [From (1)]= |¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯1α¯¯¯β||1¯¯¯¯αβ| (|β|=1 and |¯¯¯z|=|z|)= |1¯¯¯¯αβ||1¯¯¯¯αβ|=1

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon