# Properties of complex numbers

Let z be a complex number z=x+iy

x <>0 and y<>0

Prove:

1. If z+1/z is real then |z|=1

2. If |z|=1 then z+1/z is real

https://brainmass.com/math/number-theory/two-ways-prove-theorem-complex-numbers-theory-8627

#### Solution Summary

This problem demonstrates the properties of complex number and the transformation between Cartesian and polar representations.

$2.19