Chapter 1, Equations and Graphs - Section 1.5 - Complex Numbers - 1.5 Exercises: 82

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.

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