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

The complex number z is purely imaginary,if

if z-bar(z)=0 then z is purely imaginary

If z is purely real; then arg(z)=0 or pi

If roots of the equation z^(2)+az+b=0 are purely imaginary then

If the number (z-1)/(z+1) is purely imaginary, then

If the ratio (1-z)/(1+z) is purely imaginary, then

If z is a unimodular number (!=+-i) then (z+i)/(z-i) is (A) purely real (B) purely imaginary (C) an imaginary number which is not purely imaginary (D) both purely real and purely imaginary

Prove that: (i) z=overline(z) iff z is real (ii) z=-overline(z) iff z is either zero or purely imaginary.

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots.Then the equation p(p(x))=0 has A.only purely imaginary roots B.all real roots C.two real and purely imaginary roots D.neither real nor purely imaginary roots

If z^(2) + |z|^(2) = 0 , show that z is purely imaginary.