Home
Class 12
MATHS
Let z,z(0) be two complex numbers. It is...

Let `z,z_(0)` be two complex numbers. It is given that `abs(z)=1` and the numbers `z,z_(0),zbar_(0),1` and 0 are represented in an Argand diagram by the points P,`P_(0)`,Q,A and the origin, respectively. Show that `/_\POP_(0)` and `/_\AOQ` are congruent. Hence, or otherwise, prove that
`abs(z-z_(0))=abs(zbar(z_(0))-1)=abs(zbar(z_(0))-1)`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Complex Number Exercise 8|2 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Subjective Type Questions)|12 Videos

  • CIRCLE

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

Similar Questions

Explore conceptually related problems

Numbers of complex numbers z, such that abs(z)=1 and abs((z)/bar(z)+bar(z)/(z))=1 is

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

If z_1,z_2 are two complex numbers such that Im(z_1+z_2)=0,Im(z_1z_2)=0 , then:

Find the complex number z such that z^2+|z|=0

Let A,B,C be three collinear points which are such that AB.AC=1 and the points are represented in the Argand plane by the complex numbers, 0, z_(1) and z_(2) respectively. Then,

If z!=0 is a complex number, then prove that R e(z)=0 rArr Im(z^2)=0.

Let z_1a n dz_2 be two complex numbers such that ( z )_1+i( z )_2=0 and arg(z_1z_2)=pidot Then, find a r g(z_1)dot

Let z_1 and z_2 be two non - zero complex numbers such that z_1/z_2+z_2/z_1=1 then the origin and points represented by z_1 and z_2

The set of points in an Argand diagram which satisfy both abs(z)le4 and 0 le arg(z) le pi/3 , is

If z is a complex number such that |z-1|= |z+1| , show that Re(z)= 0