Answer
$106$
Work Step by Step
The complex conjugate of $a+bi$ is $a−bi$.
So the complex conjugate of $5−9i$ is $5−(−9i)$ that is, $5+9i$.
Now let's calculate the product.
$(5−9i)(5+9i)=5(5)+5(9i)+(−9i)(5)+(−9i)(9i)$ ... FOIL method
$(5−9i)(5+9i)=25+45i−45i−81i^2$
$(5−9i)(5+9i)=25+45i−45i−81(−1)$ (Substituting $i^2=−1$)
$(5−9i)(5+9i)=25+45i−45i+81$
Combining the like terms, we get
$(5−9i)(5+9i)=(25+81)+(45i−45i)$
$(5−9i)(5+9i)=106$
