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 like terms, we get
$(5-9i)(5+9i)=(25+81)+(45i-45i)$
$(5-9i)(5+9i)=106$
