Home
Class 12
MATHS
Let a ,b and c be any three nonzero comp...

Let `a ,b and c` be any three nonzero complex number. If `|z|=1 and' z '` satisfies the equation `a z^2+b z+c=0,` prove that `a .bar a` = `c .bar c` and |a||b|=`sqrt(a c( bar b )^2)`

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

If a ,b ,c are non zero complex numbers of equal modlus and satisfy a z^2+b z+c=0, hen prove that (sqrt(5)-1)//2lt=|z|lt=(sqrt(5)+1)//2.

Number of imaginary complex numbers satisfying the equation, z^2=bar(z)2^(1-|z|) is

Show that |a b c a+2x b+2y c+2z x y z|=0

Consider the equation az + b bar(z) + c =0 , where a,b,c in Z If |a| ne |b| , then z represents

If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely imaginary roots, then prove that a=b^2c dot

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y=z (b-1)y=z+x (c-1)z=x+y has a non-trivial solution, then prove that a b+b c+c a=a b c

If z be a non-zero complex number, show that (bar(z^(-1)))= (bar(z))^(-1)

If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely imaginary roots, then prove that a=b^2c

a ,b ,c are three complex numbers on the unit circle |z|=1, such that a b c=a+b+cdot Then find the value of |a b+b c+c a|dot

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar z_1 z_2