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

For two unimodular complex numbers z1 and z2, [¯¯¯¯¯z1−z2¯¯¯¯¯z2z1]−1[z1z2−¯¯¯¯¯z2¯¯¯¯¯z1]−1 is equal to

A
[z1z2¯¯¯¯¯z1¯¯¯¯¯z2]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
[1001]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
[1/2001/2]
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
none of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C [1/2001/2]
Given, |z1|=|z2|=1
z1 and z2, [¯¯¯¯¯z1z2¯¯¯¯¯z2z1]1[z1z2¯¯¯¯¯z2¯¯¯¯¯z1]1
Let A=[¯¯¯¯¯z1z2¯¯¯¯¯z2z1],B=[z1z2¯¯¯¯¯z2¯¯¯¯¯z1]
Here, |A|=z1¯z1+z2¯z2=|z1|2+|z2|2=2
|B|=z1¯z1+z2¯z2=|z1|2+|z2|2=2
Hence, A1,B1 exists
Now, adjA=CT=[z1¯¯¯¯¯z2z2¯¯¯¯¯z1]T
adjA=[z1z2¯¯¯¯¯z2¯¯¯¯¯z1]
Hence, A1=12[z1z2¯¯¯¯¯z2¯¯¯¯¯z1]
Now, adjB=[¯¯¯¯¯z1¯¯¯¯¯z2z2z1]T
adjB=[¯¯¯¯¯z1z2¯¯¯¯¯z2z1]
Hence,B1=12[¯¯¯¯¯z1z2¯¯¯¯¯z2z1]
Now, A1B1=14[z1z2¯¯¯¯¯z2¯¯¯¯¯z1][¯¯¯¯¯z1z2¯¯¯¯¯z2z1]
=14[|z1|2+|z2|200|z1|2+|z2|2]
=[120012]

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