Let `z=9+b i ,w h e r eb` is nonzero real and `i^2=-1.` If the imaginary part of `z^2a n dz^3` are equal, then `b/3` is ______.

Let z=9+bi where b is non zero real and i^(2)=-1. If the imaginary part of z^(2) and z^(3) are equal,then b^(2) equals

Let z be a complex number satisfying 2z+|z|=2+6i .Then the imaginary part of z is

Let z=9+ai, where i=sqrt(-1) and a be non-zero real. If Im(z^(2))=Im(z^(3)) , sum of the digits of a^(2) is

Let z_(1),z_(2) be two distinct complex numbers with non-zero real and imaginary parts such that "arg"(z_(1)+z_(2))=pi//2 , then "arg"(z_(1)+bar(z)_(1))-"arg"(z_(2)+bar(z)_(2)) is equal to

Let z be a complex number such that the imaginary part of z is nonzero and a=z^(2)+z+1 is real.Then a cannot take the value

Consider the equation 10 z^2-3i z-k=0,w h e r ez is a following complex variable and i^2=-1. Which of the following statements ils true? For real complex numbers k , both roots are purely imaginary. For all complex numbers k , neither both roots is real. For all purely imaginary numbers k , both roots are real and irrational. For real negative numbers k , both roots are purely imaginary.