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.

Solve |z|+z= 2+ i , where z is a complex number

solve z+2=1/(4-3i), where z is a complex number

The roots of the equation z^(4) + az^(3) + (12 + 9i)z^(2) + bz = 0 (where a and b are complex numbers) are the vertices of a square. Then The value of |a-b| is

The roots of the equation z^(4) + az^(3) + (12 + 9i)z^(2) + bz = 0 (where a and b are complex numbers) are the vertices of a square. Then The area of the square is

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

The number of solutions of the equation z^2+z=0 where z is a a complex number, 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

Find roots of the equation (z + 1)^(5) = (z - 1)^(5) .

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

For a complex number Z, if one root of the equation Z^(2)-aZ+a=0 is (1+i) and its other root is alpha , then the value of (a)/(alpha^(4)) is equal to