If `a cosalpha + i sinalpha` and the equation `az^2 + z + 1=0` has a pure imaginary root, then `tan alpha=`

If roots of the equation z^(2)+az+b=0 are purely imaginary then

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.

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.

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 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 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.

If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely imaginary roots, then prove that a=b^2c

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.

The condition that the equation az^(2)+bz+c=0 hasboth purely imaginary roots where a,b,c are non-zero complex constants,is