is it true that ||z| - |w|| \leq |z + w| ?? is it true that [itex] ||z| - |w|| \leq |z + w| [/itex]?? if so what is the proof? here is my workin so far.. please verify it thanks. We know [itex] |z+w| \leq |z|+|w| [/itex] let c = z - w, so [itex] |c+w| \leq |c|+|w| [/itex] Now z = c + w, so [itex] |z| \leq |c|+|w| [/itex] [itex] |z| \leq |z-w| + |w| [/itex] [itex] |z-w| \geq |z| -|w| [/itex] Now let d = - w, so [itex] |z - d| \geq |z| - |d| [/itex] subbing in -w for d we get, [itex] |z + w| \geq |z| - |d| [/itex] subbing in |w| for |d| since they are equal, we get [itex] |z + w| \geq ||z| - |w|| [/itex] (i added an extra modulus bracket outside the right hand side at the end of the equation). End of proof. Is this correct please? please guide me if i am wrong?