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|`

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|) .

Which of the following are correct for any two complex numbers z_1 and z_2? (A) |z_1z_2|=|z_1||z_2| (B) arg(|z_1 z_2|)=(argz_1)(arg,z_2) (C) |z_1+z_2|=|z_1|+|z_2| (D) |z_1-z_2|ge|z_1|-|z_2|

If z_1,z_2 are nonzero complex numbers then |(z_1)/(|z_1|)+(z_2)/(|z_2|)|le2 .

For any two complex number z_(1) and z_(2) prove that: |z_(1)+z_(2)|>=|z_(1)|-|z_(2)|

For any two complex number z_(1) and z_(2) prove that: |z_(1)-z_(2)|>=|z_(1)|-|z_(2)|

For any two complex number z_(1) and z_(2) prove that: |z_(1)+z_(2)|<=|z_(1)|+|z_(2)|

For any two complex number z_(1) and z_(2) prove that: |z_(1)-z_(2)|<=|z_(1)|+|z_(2)|

For complex numbers z_1 = 6+3i, z_2=3-I find (z_1)/(z_2)