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)`

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

The number of complex numbers z such that |z|=1 and |z/ barz + barz/z|=1 is arg(z) in [0,2pi)) then a. 4 b. 6 c. 8 d. more than 8

Let a , b , c be distinct complex numbers with |a|=|b|=|c|=1 and z_(1) , z_(2) be the roots of the equation az^(2)+bz+c=0 with |z_(1)|=1 . Let P and Q represent the complex numbers z_(1) and z_(2) in the Argand plane with /_POQ=theta , o^(@) lt 180^(@) (where O being the origin).Then

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

Consider the equation az+b bar(z)+c=0" ""where" " "a,b,cin Z If |a|=|b| and bar(ac)!=bar(bc), then z has

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

Solve bar(z)=iz^(2) (z being a complex number)

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

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 -pi b. pi/2 c. 0 d. pi/2 e. pi