Respuesta :

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]

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