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

Let z and w be two complex numbers such that |z|1, |ω|1 and |z+iω|=|zi¯ω|=2, then z equals

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

The correct option is C 1 or -1
Given, |z+iω|=|zi¯ω|=2|z(iω)|=|z(i¯ω)|=2|z(iω)|=|z(i¯ω)|
z lies on the perpendicular bisector of the line joining iω and i¯ω. Since i¯ω is the mirror image of iω in the x-axis, the locus of z is the x-axis.
Let z=x+iy and y=0.Now, |z|1x2+0211x1.
z may take values given in option (c).

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