Home
Class 12
MATHS
Let w=(sqrt(3)+i)/(2)andp={w^(n):n =1 , ...

Let `w=(sqrt(3)+i)/(2)andp={w^(n):n =1 , 2 , 3 , .....}. "Further " H_(1)={z in CC :Rezgt(1)/(2)}andH_(2)={zin CC:Rezlt(-1)/(2)}`, where `CC` is the set of all complex numbers , If `z_(1)inpcapH_(1),z_(2)inpcapH_(2) andO " represents the orgin,then " anglez_(1)Oz_(2)` =

A

`(pi)/(2)`

B

`(pi)/(6)`

C

`(2pi)/(3)`

D

`(5pi)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Similar Questions

Explore conceptually related problems

For all complex numbers z_(1),z_(2) satisfying |z_(1)|=12 and |z_(2) -3-4i|=5, then minimum value of |z_(1)-z_(2)| is-

If z_(1)andz_(2) be two non-zero complex numbers such that (z_(1))/(z_(2))+(z_(2))/(z_(1))=1 , then the origin and the points represented by z_(1)andz_(2)

If z_(1),z_(2) are two complex numbers , prove that , |z_(1)+z_(2)|le|z_(1)|+|z_(2)|

If z_(1) , z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 and iz_(1)=Kz_(2) , where K in R , then the angle between z_(1)-z_(2) and z_(1)+z_(2) is

Let z_(1)=2+3iandz_(2)=3+4i be two points on the complex plane . Then the set of complex number z satisfying |z-z_(1)|^(2)+|z-z_(2)|^(2)=|z_(1)-z_(2)|^(2) represents -

Let z_1=2+3i and z_2=3+4i be two points on the complex plane then the set of complex numbers z satisfying abs(z-z_1)^2+abs(z-z_2)^2=abs(z_1-z_2)^2 represents

If z_(1) , z_(2) are complex numbers such that Re(z_(1))=|z_(1)-2| , Re(z_(2))=|z_(2)-2| and arg(z_(1)-z_(2))=pi//3 , then Im(z_(1)+z_(2))=

An operation ** on the set of all complex numbers CC is defined by z_(1)**z_(2)=sqrt(z_(1)z_(2)) for all z_(1),z_(2)inCC . Is ** a binary operation on CC ?

If the complex numbers z_(1),z_(2),z_(3) represents the vertices of an equilaterla triangle such that |z_(1)|=|z_(2)|=|z_(3)| , show that z_(1)+z_(2)+z_(3)=0

If z_(1)+z_(2) are two complex number and |(barz_(1)-2bar z_(2))/(2-z_(1)barz_(2))|=1, |z_(1)| ne , then show that |z_(1)|=2 .