Answer
The statement is true. See below for proof.
Work Step by Step
We are given that $z=a+bi$:
$z-\overline{z}=(a+bi)-\overline{(a+bi)}=a+bi-(a-bi)=a+bi-a+bi=2bi+a-a=2bi$
We know that $b$ is a real number, so $2bi$ is a pure imaginary number.
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305115546
ISBN 13:
978-1-30511-554-5
Chapter 1, Equations and Graphs - Section 1.5 - Complex Numbers - 1.5 Exercises - Page 131: 82
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