For any two complex numbers `z_1` and `z_2` , prove that `R e(z_1z_2)=R e""z_1""R e z_2-|m z_1|m 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

For any two complex numbers z_1 and z_2 prove that Re(z_1z_2) = Re(z_1)Re(z_2) - Im(z_1)Im(z_2)

For any two complex numbers z_1 and z_2 , prove that Re(z_1z_2)=Re(z_1) Re(z_2)-Im(z_1) Im(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

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

For any two complex numbers z1 and z2 ,prove that |z1.z2|=|z1|.|z2|

For any two complex numbers, z_1 and z_2 , prove that Re( z_1 z_2 ) = [(Re( z_1 ). Re( z_2 )] - [Im( z_1 ). Im( z_2 )]

For any two complex numbers z_(1)" and "z_(2) prove that (i) Re(z_(1)z_(2))=Re(z_1) Re(z_2)-Im(z_1)Im(z_2) .

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|geq|z_1|-|z_2|