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 haly no root which is either purely real or purely imaginary.

Prove that : z= -bar(z) iff z is either zero or purely imaginary.

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

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.