Prove `Im(z_1 z_2)=Rez_1.Imz_2+Rez_2.Imz_1`

Show that Re(z_1z_2)=Rez_1Rez_2-Im z_1Imz_2 Im(z_1z_2)=Re z_1 Im z_2+Re z_2 Im z_1

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) .

Prove Im (z_ (1) z_ (2)) = Rez_ (1) .Im z_ (2) + Rez_ (2) .Im z_ (1)

Define addition and multiplication of two complex numbers z_1 and z_2 . Hence show that : I_m (z_1 z_2)=R_e (z_1)I_m (z_2)- I_m (z_1)R_e(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 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 Im(z_(1)z_(2))=Re(z_1) Im(z_2)+ Im(z_1)Re(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)- I_m (z_1)I_m(z_2) .