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

If complex numbers z1 and z2 both satisfy z+¯¯¯z=2|z1| and arg(z1z2)=π3, then the value of Im(z1+z2) is
(Im(z) denotes the imaginary part of z)

A
sinπ3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
cosec π3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
tanπ3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
cotπ3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B cosec π3
Let z=x+iy
z+¯¯¯z2=|z1|
x2=(x1)2+y2
y2=2x1
Let z1(t21+12,t1) and z2(t22+12,t2)
arg(z1z2)=π3
t2t1(t22t212)=3
2t1+t2=3
Im(z1+z2)=t1+t2=23

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