p and q are complex numbers such that |q|=4√5 and |p+q|=9√2. On what interval must |p| fall on?

Answer 1

Caucy's : Front Half

|p+ q| <= |p| + |q|

9/2 <= |p| +4* sqrt(5)

9/2 - 4*sqrt(5) <= |p|

Caucy's : Back Half:

-|p|-|q| <= |p+q|

-|p| - 4*sqrt(5) <= 9/2

-|p| <= 9/2 + 4 * sqrt(5)

|p| >= -9/2 - 4*sqrt(5)

-9/2 - 4*sqrt(5) <= |p| < 9/2 + 4 * sqrt(5)