(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Where z is a complex number:

|4+z| - |4-z| = 6

Prove that |4+z|^2 - |4-z|^2 >= 48

2. The attempt at a solution

|4+z| = 6 + |4-z|

|4+z|^2 = 36 + |4-z|^2 + 12|4-z|

|4+z|^2 - |4-z|^2 = 36 + 12|4-z|

From here, I figure if I can prove that |4-z| >= 1, I can prove that |4+z|^2 - |4-z|^2 >=48

Any pointers as to how I can do this? Or am I approaching this from the wrong angle?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# |4+z| - |4-z| = 6, prove |4+z|^2 - |4-z|^2 >= 48

**Physics Forums | Science Articles, Homework Help, Discussion**