Find the range of real number `alpha` for which the equation `z+alpha|z-1|+2i=0` has a solution.

Let S be the set of the non zero real numbers alpha such that the quadratic equation alphax^(2)-x+alpha=0 has two distinct real roots x_(1)andx_(2) satisfying the inequlity |x_(1)-x_(2)|lt1 . Which of the following intervals is (are) a subset (s) of s?

Let S be the set of all non-zero real numbers alpha such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1 and x_2 satisfying the inequality abs(x_1-x_2)lt1 . Which of the following intervals is (are) a subset(s) of S ?

Prove that the equation Z^3+i Z-1=0 has no real roots.

The complex number z satisfying the equation |z-i|=|z+1|=1 is

The number of real values of alpha for which the system of equations {:(x+3y+5z=alphax),(5x+y+3z=alpha y),(3x+5y+z= alpha z):} has infinite number of solutions is

Find the number of complex numbers which satisfies both the equations |z-1-i|=sqrt(2)a n d|z+1+i|=2.

The value of |alpha| for which the system of equation alphax+y+z=alpha-1 x+alphay+z=alpha-1 x+y+alphaz=alpha-1 has no solution , is "____"

Find the number of values of lambda for which the system of equations lambdax+y+z=1,x+lambday+z=lambda and x+y+lambdaz=lambda^2 has infinite number of solutions .

Find the real values of K for which the following system of linear equations has no-trivial solution: x - ky - z = 0, kx - y - z = 0, x + y-z = 0

Find the real values of lambda for which the following system of linear equations has non -trivial solutions: x+y-3z=0,( 1+lambda)x+(2+lambda)y-8z=0 , x-(1+lambda)y+(2+lambda)z=0 .