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## Homework Statement

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?