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

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.

If a,b,c are nonzero complex numbers of equal moduli and satisfy az^(2)+bz+c=0 hen prove that (sqrt(5)-1)/2<=|z|<=(sqrt(5)+1)/2

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

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

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

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)

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)

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 and c are complex numbers and z satisfies az^(2)+bz+c=0 , prove that abs(a)abs(b)=sqrt(a(bar(b))^(2)c) and abs(a)=abs(c) Leftrightarrow abs(z)=1 .