Show that for ` z epsilon C, |\z|=0 ` if and only if ` z=0`

Show that if iz^3+z^2-z+i=0 , then |z|=1

Show that if iz^3+z^2-z+i=0 , then |z|=1

Show that |a b c a+2x b+2y c+2z x y z|=0

A relation R on the set of complex numbers is defined by z_1 R z_2 if and only if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

If z_(1), z_(2), z_(3), z_(4) are complex numbers, show that they are vertices of a parallelogram In the Argand diagram if and only if z_(1) + z_(3)= z_(2) + z_(4)

If z=x+i y , then show that z bar z +2(z+ bar z )+a=0 , where a in R , represents a circle.

The complex numbers z_1, z_2 and the origin form an equilateral triangle only if (A) z_1^2+z_2^2-z_1z_2=0 (B) z_1+z_2=z_1z_2 (C) z_1^2-z_2^2=z_1z_2 (D) none of these

Prove that the complex numbers z_(1),z_(2) and the origin form an equilateral triangle only if z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0 .

Solve :z^2+|z|=0 .

Let S=S_1 nn S_2 nn S_3 , where s_1={z in C :|z| 0} and S_3={z in C : Re z > 0} Area of S=