" i) "z^(3)-3z^(2)+4

If z = i(i + sqrt(2)) , then value of z^(4) + 4z^(3) + 6z^(2) + 4z is

If z=2-isqrt(7) , then show that 3z^(3)-4z^(2)+z+88=0

If the polynomials az^(3)+4z^(2)+3z-4 and z^(3)-4z+a leave the same remainder when divided by z-3, find the value of a.

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 .

If z=3-4i then z^(4)-3z^(3)+3z^(2)+99z-95 is equal to

If z_(1),z_(2),z_(3),z_(4) are the roots of equation z^(4)+z^(3)+z^(2)+z+1=0, then prod_(i=1)^(4)(z_(i)+2)

If z_(1),z_(2),z_(3),z_(4) are the roots of the equation z^(4)+z^(3)+z^(2)+z+1=0, then the least value of [|z_(1)+z_(2)|]+1 is (where [.] is GIF.)

Show that the equation Z^(4)+2Z^(3)+3Z^(2)+4Z+5=0 haly no root which is either purely real or purely imaginary.