[" For any complex number "z," prove that "],[|Re(z)|+|Im(z)|<=sqrt(2)|z|]

For any complex number z,prove that |Re(z)|+|I_m(z)|le\sqrt 2 |z|

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

For any complex number z, prove that : -|z| leR_e (z) le |z| .

For any complex number z, prove that : -|z| leI_m (z) le |z| .

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_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 )] - [Im( z_1 ). Im( z_2 )]