If one root of the equation `z^2-a z+a-1= 0` is (1+i), where a is a complex number then find the root.

Number of solutions of the equation z^3+[3(barz)^2]/|z|=0 where z is a complex number is

If one root of the equation x^2+(1-3i)x-2(1+i)=0 is -1+i, then the other root is

let z_1 and z_2 be roots of the equation z^2+pz+q=0 where the coefficients p and q may be complex numbers let A and B represnts z_1 and z_2 in the complex plane if angleAOB=alpha ne 0 and OA=OB where 0 is the origin prove that p^2=4qcos^2(alpha/2)

If one root of the equation x^(2)+(1-3i)x-2(1+i)=0 is -1+i , then the other root is

If z=-i-1 is a complex number,then arg (z) will be

Let a , b , c be distinct complex numbers with |a|=|b|=|c|=1 and z_(1) , z_(2) be the roots of the equation az^(2)+bz+c=0 with |z_(1)|=1 . Let P and Q represent the complex numbers z_(1) and z_(2) in the Argand plane with /_POQ=theta , o^(@) lt 180^(@) (where O being the origin).Then

One of the roots of equation (z^(2))/(z)=2 is ______ .

Show that the roots of the equation 9x^2-24x+25=0 are complex numbers, solving the equation show that the complex roots are conjugate complex numbers.

Find the square root of the complex number z=2i .

Find the square root of the complex number z=8i .