Find the truth 7Algebra Level 5
Read the following statements.
I) It is known that \(x\) is a member of the set of complex numbers ( which includes all real numbers also ), then \(|x|\) is always a positive real.
II) If \(f\left( g\left( x \right) \right) =x \) for all \(x\), then \(g\left( f\left( x \right) \right) =x \) for all \(x\).
III) It is not possible to have a complex number \(z\), such that \(\left| z \right| =\left| z+1 \right| =\left| z-1 \right| \).
Which of the above statements are true?