If the equation `z^3 + (3 + l)(z^2) - 3z - (m + l)= 0,` `m in R` , has at least one real root, then sum of possible values of m, is

An atomic orbital has l= 3. What are the possible values of m?

Solve the equation z^3= z (z!=0)dot

If the equation x^(2)+12+3sin(a+bx)+6x=0 has atleast one real solution, where a, b in [0,2pi] , then the value of a - 3b is (n in Z)

Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0,w h e r em in Rdot Suppose the equation has a real root. Then root non-real root.

If z is a complex number satisfying z^4+z^3+2z^2+z+1=0 then the set of possible values of z is

Show that the equation z^(3) + 2 bar(z) = 0 has five solutions.

If |z|=1 and z ne +-1 , then one of the possible value of arg(z)-arg(z+1)-arg(z-1) , is

Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x + 5y + lambdaz=-3 has at least one solution for any real number lambda. Find the set of solutions of lambda =-5

If the system of equation {:(,x-2y+z=a),(2x+y-2z=b),and,(x+3y-3z=c):} have at least one solution, then