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

If z is a Complex number satisfying the equation |z(1+i)|2=2 and ω=2z, then the locus traced by ω in the complex plane is

A
xy1=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x+y1=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
xy+1=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
x+y+1=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B x+y1=0
Given:
ω=2z
z=2ω
z(1+i)=2ω(1+i)
|z(1+i)|2=2ω(1+i)2=2
Let ω=x+iy

2x+iy(1+i)2=2

2(xiy)(1+i)(x2+y2)x2+y2=2

(2xx2y2)i(2yx2y2)x2+y2=2

(2x(x2+y2))2+(2yx2y2)2=(2(x2+y2))2

4x24x(x2+y2)4y(x2+y2)=4y2

4(x2+y2)=4(x2+y2)(x+y)

x+y=1x+y1=0

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