If `z_1` and `z_2 (ne 0)` are two complex numbers, prove that : `|z_1 z_2|= |z_1||z_2|`.

If z_1 and z_2 (ne 0) are two complex numbers, prove that : |z_1/z_2|= (|z_1|)/ (|z_2|), z_2 ne 0 .

If z_1 and z_2 are two complex numbers and c >0 , then prove that |z_1+z_2|^2lt=(1+c)|z_1|^2+(1+c^(-1))|z_2|^2dot

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

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.

If z_1, z_2, z_3 are complex numbers such that |z_1|= |z_2|= |z_3| =|1/z_1+1/z_2+1/z_3|=1, |z_1+z_2+z_3| is :

If z_1 and z_2 are two complex number such that |(z_1-z_2)/(z_1+z_2)|=1 , Prove that iz_1/z_2=k where k is a real number Find the angle between the lines from the origin to the points z_1 + z_2 and z_1-z_2 in terms of k

If z_1, z_2 are two complex numbers satisfying the equation |(z_1 +z_2)/(z_1 -z_2)|=1 , then z_1/z_2 is a number which is :

If z_1=a + ib and z_2 = c + id are complex numbers such that |z_1|=|z_2|=1 and Re(z_1 bar z_2)=0 , then the pair of complex numbers omega_1=a+ic and omega_2=b+id satisfies a. |omega_(1)|=1 b. |omega_(2)|=1 c. Re(omega_(1)baromega_(2))=0 d. None of these