Number of solutions of the equation `z^(2)+|z|^(2)=0` is

The number of solutions of equation z^(2) + barz = 0 , where z in C are

Number of positive unequal integral solutions of the equation x+y+z=12 is

Let z_(1) and z_(2) be two roots of the equation z^(2)+az+b=0 , z being complex number, assume that the origin z_(1) and z_(2) form an equilateral triangle , then

The number of integral solutions of equation x+y+z+t=29, when x >= 1, y >= 2, z>=2, 3 and t >= 0 is

Let z be a complex number satisfying the equation z^(2)-(3+i)z+lambda+2i=0, whre lambdain R and suppose the equation has a real root , then find the non -real root.

Solve the equation z^(2)=bar(z) where z=x+iy

If z_(1),z_(2) are two complex numbers satisfying the equation : |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then (z_(1))/(z_(2)) is a number which is

Let z_1 \and\ z_2 be the roots of the equation z^2+p z+q=0, where the coefficients p \and \q may be complex numbers. Let A \and\ B represent z_1 \and\ z_2 in the complex plane, respectively. If /_A O B=theta!=0 \and \O A=O B ,\where\ O is the origin, prove that p^2=4q"cos"^2(theta//2)dot

The complex number z which satisfies the Equation |(i+z)/(i-z)|=1 lies on

All complex number z which satisfy the equation |(z-6 i)/(z+6 i)|=1 lie on the