Show that for any two non zero complex numbers `z_1,z_2 (|z_1|+|z_2|)|z_1\|z_1|+z_2\|z_2||le2|z_1+z_2|`

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Prove that for nonzero complex numbers |z_1+z_2| |frac(z_1)(|z_1|)+frac(z_2)(|z_2|)|le2(|z_1|+|z_2|) .

For any two complex numbers z_1 and z_2 , prove that |z_1+z_2| =|z_1|-|z_2| and |z_1-z_2|>=|z_1|-|z_2|

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

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

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

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar z_1 z_2

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2 +|\z_1-z_2|^2=2[|\z_1|^2+|\z_2|^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 , we have |z_1+z_2|^2=|z_1|^2+|z_2|^2 , then