6z^(3)+13z^(2)+2z-5

Simplify combining like terms: -z^(2) +13z^(2) - 5z + 7z^(3) -15z

If z = 3 + 2i , prove that z^(2) - 6z + 13 = 0 and hence deduce that 3z^(3) - 13z^(2) + 9z + 65 = 0 .

The sum of the distinct real roots of polynomial 72-36z-26z^(2)+13z^(3)+2z^(4)-z^(5)=0 will be

(z^(2)+13)(z^(2)-5)= ____

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

Let z_(1), z_(2), z_(3) be the roots of iz^(3) + 5z^(2) - z + 5i = 0 , then |z_(1)| + |z_(2)| + |z_(3)| = _____________.

Add the following expressions: 3z^(3)-z^(2)+5, 1-2z+z^(2), 3+2z-z^(3)

If z=3-2i then show that z^(2)-6z+13=0 Hence find the value of z^(4)-4z^(3)+6z^(2)-4z+17

If z_(1) = 3, z_(2) = -7i, and z_(3) = 5 + 4i, show that (z_(1) + z_(2)) z_(3) = z_(1) z_(3) + z_(2) z_(3)

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 .