For any complex number z=x+ iy,define (z...

For any complex number z=x+ iy,define (z)=|x|+|y|. If z_(1) and z_(2) are any two complex numbers,then (1) (z_(1)+z_(2))lt=(z_(1))+(z_(2)) (2) (z_(1)+z_(2))=(z_(1))+(z_(2)) (3) (z_(1)+z_(2))gt=(z_(1))+(z_(2)) (4) (z_(2)-z_(1))=(z_(2))-(z_(1))

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