If two complex numbers `z_1,z_2` are such that `|z_1| = |z_2|`, is it then necessary that `z_1 = z_2`?

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

If the complex number z_1 and z_2 be such that arg(z_1)-arg(z_2)=0 , then show that |z_1-z_2|=|z_1|-|z_2| .

If z_1a n dz_2 are two nonzero complex numbers such that |z_1+z_2|=|z_1|+|z_2|, then a rgz_1-a r g z_2 is equal to

If z is any complex number, prove that : |z|^2= |z^2| .

For any two complex numbers z_1 and z_2 , prove that Re (z_1 z_2) = Re z_1 Re z_2 - Imz_1 Imz_2

Define addition and multiplication of two complex numbers z_1 and z_2 . Hence show that : R_e (z_1+ z_2)=R_e (z_1)+R_e (z_2) .

For any complex number z, the minimum value of |z|+|z-1| is :

Consider z_(1)andz_(2) are two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| Statement -1 amp (z_(1))-amp(z_(2))=0 Statement -2 The complex numbers z_(1) and z_(2) are collinear. Check for the above statements.

Define addition and multiplication of two complex numbers z_1 and z_2 . Hence show that : I_m (z_1+ z_2)=I_m (z_1)+I_m(z_2) .