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)`

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 z is a non zero complex,number then |(|z|^(2))/(zz) is equal to |(z)/(z)| b.|z| c.|z| d.none of these

The number solutions of the equation |z|^(2)+4bar(z)=0(A)2(B)4(C)6(D)3

If n is a positive integer greater than unity z is a complex number satisfying the equation z^(n)=(z+1)^(n), then

Number of imaginary complex numbers satisfying the equation, z^2=bar(z)2^(1-|z|) is (A) 0 (B) 1 (C) 2 (D) 3

Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the complex number z=x+i y satisfies I m((a z+b)/(z+1))=y , then which of the following is (are) possible value9s) of x? (a)-1-sqrt(1-y^2) (b) 1+sqrt(1+y^2) (c)-1+sqrt(1-y^2) (d) -1-sqrt(1+y^2)

Let A,B,C be three sets of complex numbers as defined below.A={z:|z+1| =1} and C={z:|(z-1)/(z+1)|>=1}