MathDB

Re(z^n)>Im(z^n), for any n, implies z is a positive real

Source:

October 28, 2019

complex numbersalgebra

Problem Statement

Let be a complex number

z

having the property that

\Re \left( z^n \right) >\Im \left( z^n \right) ,

for any natural numbers

n.

Show that

z

is a positive real number.
Laurențiu Panaitopol