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

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

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

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

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

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

For a complex number z, the equation z^(2)+(p+iq)z r+" is "=0 has a real root (where p, q, r, s are non - zero real numbers and i^(2) = -1 ), then

Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0\ ,where m in Rdot . Suppose the equation has a real root. Then find the value of m

Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0\ ,where m in Rdot . Suppose the equation has a real root. Then the value of m is-

For a complex number z, the equation z^(2)+(p+iq)z+ r+" is "=0 has a real root (where p, q, r, s are non - zero real numbers and i^(2)-1 ), then

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.