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

Similar Questions

Explore conceptually related problems

If z is any complex number such that |z+4|lt=3, then find the greatest value of |z+1|dot

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

If z is a complex number such that |z| ge 2 , then the minimum value of |z+(1)/(2)| .

Find the value of k so that the equation 49x^(2) - kx -81 =0 has one root as the negative of the other.

Find the value of q so that the equations 2x^(2) - 3qx + 5q =0 has one root which is twice the other.

If z is a complex number such that |z|=1, z ne 1 , then the real part of |(z-1)/(z+1)| is

Find the value of p so that the equations 4x^(2) - 8px +9=0 has roots whose difference is 4.

What is the value of k if the equation x^(2) +4x +(k +2) = 0 has one root equal to zero .

Find the value of k for which the quadratic equations 9x^(2) - 24x+ k=0 has equal roots.

If z is a complex number with |z|=1 and z+(1)/(z)=x+iy , then xy=