The correct questions is simplify the expression and write in standard form
[tex] \frac{(2-4i)(3+5i)}{(3+i)} [/tex]
First we need to simplify the numerator of the fraction.
(2 - 4i)(3 + 5i) = 6 +10i - 12i -20i² = 6 - 2i + 20 = 26 - 2i
So the expression becomes:
[tex] \frac{26-2i}{3+i} [/tex]
In order to remove the iota sign from denominator, we multiply and divide the fraction by its conjugate.
[tex] \frac{26-2i}{3+i} * \frac{3-i}{3-i} \\ \\
= \frac{78-26i-6i+2i^{2} }{9-i^{2} } \\ \\
= \frac{76-32i}{10} \\ \\
= \frac{38}{5}- \frac{16}{5}i [/tex]
