CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the lines a¯¯¯z+¯¯¯az+b=0 and c¯¯¯z+¯¯cz+d=0 are mutually perpendicular, where a and c are non zero complex numbers, while b and d are real numbers, then

A
a¯¯¯a+c¯¯c=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a¯¯c is purely imaginary
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
arg(ac)=±π2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
a¯¯¯a=c¯¯c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C arg(ac)=±π2
Let a=a1+ia2 and c=c1+ic2.
Then, a1a2×c1c2=1
a1c1+a2c2=0
(a+¯¯¯a2)(c+¯¯c2)+(a¯¯¯a2i)(c¯¯c2i)=0
a¯¯c+¯¯¯ac=0 (1)
a¯¯c is purely imaginary.

From (1), we have
ac=¯¯¯a¯¯c
ac+¯¯¯a¯¯c=0
ac is purely imaginary.
arg(ac)=±π2


flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Polar Representation of a Complex Number
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon