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.`

The nonzero complex number Z satisfying Z=iZ^(2) is

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 z_(1) and z_(2) are two complex numbers such that |z_(1)| lt 1 lt |z_(2)| , then prove that |(1- z_(1)barz_(2))//(z_(1)-z_(2))| lt 1

If z_1 and z_2 are two complex numbers such that |z_1|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

Modulus of nonzero complex number z satisfying bar(z)+z=0 and |z|^(2)-4zi=z^(2) is

Find a complex number z satisfying the equation z+sqrt(2)|z+1|+i=0

If z_1,z_2 are nonzero complex numbers then |(z_1)/(|z_1|)+(z_2)/(|z_2|)|le2 .

Find the complex number z satisfying Re(z^(2)=0),|z|=sqrt(3)

If a complex number z satisfies z + sqrt(2) |z + 1| + i=0 , then |z| is equal to :