Factorize the expressions and divide them as directed : `26z^3(32z^2-18) ÷ 13z^2(4z-3)`.

Subtract the second expression from the first expression: x+2y+z , -x-y-3z

If z^(2) + z + 1 = 0 , where z is a complex number , prove that ( z + 1/z)^(2) + ( z^(2) + 1/z^(2)) + (z^(3) + 1/z^(3))^(2) + (z^(4) + 1/z^(4))^(2) + (z^(5) + 1/z^(5)) ^(2) + ( z^(6) + 1/z^(6)) = 12 .

Assertion (A) : The origin and the roots of the equation x^(2) + ax + b = 0 form an equilateral triangle if a^(2) = 3b Reason (R) : If z_(1) , z_(2) , z_(3) are vertices of an equilateral triangle then z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = z_(1) z_(2) + z_(2) z_(3) + z_(3) z_(1)

If z_(1) , z_(2) , z_(3) are the vertices of an equilateral triangle with centroid at z_0 show that z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3 z_(0)^(2)

The matrix form of the system of equations 2x-y+8z=13,3x+4y+5z=18 , 3x-2y-4z=-13 is

If z = 3 + 3i then, z^(2)+z+15 =

The shortest distance between the z-axis and the line x+y+2z-3=0=2x+3y+4z-4 , is :