For what values is the expression always real?

[Bashyboy]

Homework Statement

I have the expression $a_2 \overline{\beta} + a_3 \beta$ involving complex variables, where $|\beta| \le 1$. I was wondering, is it possible to determine for what $a_2$ and $a_3$ the expression is always real, for every $\beta$ satisfying $|\beta| \le 1$; or is there insufficient information?

Homework Equations

The Attempt at a Solution

 

[Mark44]

An attempt is required. Please start a new thread that includes what you have tried.
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