Home
Class 12
MATHS
If |z1+z2|^2=|z1|^2+|zz|^2 then...

If `|z_1+z_2|^2=|z_1|^2+|z_z|^2` then

A

`z_1/z_2` is purely real

B

`z_1/z_2` is purely imaginary

C

`z_1 bar(z)_2 +z_2bar(z)_1=0`

D

amp `z_1/z_2` may be equal to `pi/2`

Text Solution

Verified by Experts

The correct Answer is:
B,C,D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED|65 Videos

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -I) PREVIOUS YEAR - JEE MAIN|12 Videos

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 2 (LEVEL -I) OBJECTIVE PROBLEMS - JEE MAIN|21 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

Similar Questions

Explore conceptually related problems

If z_1,z_2,z_3 be the vertices of a triangle ABC such that |z_1|=|z_2|=|z_3| and |z_1+z_2|^2= |z_1|^2+|z_2|^2, then |arg, ((z_3-z_1)/(z_3-z_2))|= (A) pi/2 (B) pi/3 (C) pi/6 (D) pi/4

Prove that |z_1+z_2|^2 = |z_1|^2 + |z_2|^2 if z_1/z_2 is purely imaginary.

Statement I: If |z_1+z_2|=|z_1|+|z_2|, then Im(z_1/z_2)=0 (z_1,z_2 !=0) Statement II: If |z_1+z_2|=|z_1|+|z_2| then origin, z_1, z_2 are collinear with 'z_1' and z_2 lies on the same side of the origin (z_1,z_2 !=0)

Prove that |z_1+z_2|^2+|z_1-z_2|^2 =2|z_1|^2+2|z_2|^2 .

Let z_1=r_1(costheta_1+isintheta_1)a n dz_2=r_2(costheta_2+isintheta_2) be two complex numbers. Then prove that |z_1+z_2|^2=r1 2+r2 2+2r_1r_2cos(theta_1-theta_2) or |z_1+z_2|^2=|z_1|^2+|z_2|^2+2|z_1||z_2|^()_cos(theta_1-theta_2) |z_1-z_2|^2=r1 2+r2 2-2r_1r_2cos(theta_1-theta_2) or |z_1-z_2|^2=|z_1|^2+|z_2|^2-2|z_1||z_2|^()_cos(theta_1-theta_2)

Prove that |1-barz_1z_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|z_2|^2) .

If z_1,z_2,z_3 are three complex numbers such that |z_1|=|z_2|=|z_3|=1 , find the maximum value of |z_1-z_2|^2+|z_2-z_3|^2+|z_3+z_1|^2