If a is a complex number such that `|a|=1`, then find thevalue of a, so that equation `az^2 + z +1=0` has one purely imaginary root.

If z is a complex number such that |z|>=2 then the minimum value of |z+1/2| is

lf z(!=-1) is a complex number such that [z-1]/[z+1] is purely imaginary, then |z| is equal to

The value of a for which the equation (1-a^2)x^2+2ax-1=0 has roots belonging to (0,1) is

If z is a complex number satisfying the relation ∣z+1∣=z+2(1+i) then z is

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

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has only purely imaginary roots at real roots two real and purely imaginary roots neither real nor purely imaginary roots

If p ,q , in {1,2,3,4}, then find the number of equations of the form p x^2+q x+1=0 having real roots.

Find the roots of the equation x+(1)/(x)=3, x ne 0

If (z-1)/(z+1) is purely imaginary number (zne-1) then find the value of |z|.