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 z is a complex number such that |z|geq2 , then the minimum value of |z+1/2|

4 x^2-2 x+a=0, has one roots then find the value of a ?

Consider the quadratic equation az^(2)+bz+c=0 where a,b,c are non-zero complex numbers. Now answer the following. The condition that the equation has both roots purely imaginary is

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

The number of real roots of the equation e^(x - 1) + x - 2 = 0 is

Find the values of m for which roots of equation x^(2)-mx+1=0 are less than unity.

Solve that equation z^2+|z|=0 , where z is a complex number.

If two complex numbers z_1,z_2 are such that |z_1|= |z_2| , is it then necessary that z_1 = z_2 ?

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

If alpha is a complex constant such that alpha z^2+z+bar( alpha)=0 has a real root, then