prove that `|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|lt=|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|

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

Prove that |z_1+z_2|^2=|z_1|^2+|z_2|^2, ifz_1//z_2 is purely imaginary.

If z_1a n dz_2 are complex numbers and u=sqrt(z_1z_2) , then prove that |z_1|+|z_2|=|(z_1+z_2)/2+u|+|(z_1+z_2)/2-u|

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

(v) |(z_1)/(z_2)|=|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]

Given that |z_1+z_2|^2=|z_1|^2+|z_2|^2 , prove that z_1/z_2 is purely imaginary.