Home
Class 12
MATHS
If z1 + z2 + z3 + z4 = 0 where bi in ...

If `z_1 + z_2 + z_3 + z_4 = 0` where `b_i in R` such that the sum of no two values being zero and `b_1 z_1+b_2z_2 +b_3z_3 + b_4z_4 = 0` where `z_1,z_2,z_3,z_4` are arbitrary complex numbers such that no three of them are collinear, prove that the four complex numbers would be concyclic if `|b_1b_2||z_1-z_2|^2=|b_3b_4||z_3-z_4|^2`.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise EXAMPLE|10 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise EXAMPLE(Single integer answer type questions)|1 Videos

  • CIRCLE

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

  • CONTINUITY AND DIFFERENTIABILITY

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

Similar Questions

Explore conceptually related problems

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

If z_1 and z_2 (ne 0) are two complex numbers, prove that : |z_1 z_2|= |z_1||z_2| .

If two complex numbers z_1,z_2 are such that |z_1|= |z_2| , is it then necessary that z_1 = z_2 ?

The points z_(1),z_(2),z_(3),z_(4) in the complex plane are the vertices of a parallelogram taken in order if and only if

Solve that equation z^2+|z|=0 , where z is a complex number.

If z_1a n dz_2 are two nonzero complex numbers such that |z_1+z_2|=|z_1|+|z_2|, then a rgz_1-a r g z_2 is equal to

Find the difference of the complex numbers : z_1=- 3 + 2i and z_2= 13-i .

z_(1) and z_(2) are the roots of the equation z^(2) -az + b=0 where |z_(1)|=|z_(2)|=1 and a,b are nonzero complex numbers, then

If z_1,z_2 are comples numbers such that (2 z_1)/(3z_2) is purely imaginary number, then find |(z_1-z_2)/ (z_1+ z_2)| .