Question

What is the standard form of (2-4i)(3+5i) divided by (3+i)

Answer 1

First we need to simplify the numerator of the fraction

(2 - 4i)(3 + 5i)
= 6 +10i - 12i - 20i²
= 6 - 2i + 20
= 26 - 2i

So now the fraction becomes:


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

In order to convert the fraction to standard form, we need to multiply and divide the fraction by the conjugate of the denominator as shown below:


`(26-2i)/(3+i)* (3-i)/(3-i) \\ \\ = (78-26i-6i+2i^(2) )/(9-i^(2) ) \\ \\ = (78-32i-2)/(9+1) \\ \\ = (76-32i)/(10) \\ \\ = (76)/(10)- (32i)/(10) \\ \\ = (38)/(5)- (16)/(5)i`