Question

(2-4)(3+5i)/(3+i) morning

Answer 1

The correct questions is simplify the expression and write in standard form


`((2-4i)(3+5i))/((3+i))`

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:


`(26-2i)/(3+i)`

In order to remove the iota sign from denominator, we multiply and divide the fraction by its conjugate.


`(26-2i)/(3+i) * (3-i)/(3-i) \\ \\ = (78-26i-6i+2i^(2) )/(9-i^(2) ) \\ \\ = (76-32i)/(10) \\ \\ = (38)/(5)- (16)/(5)i`