(simplest form a+bi) (8)/(6 - i) ​

Question

(simplest form a+bi)

`(8)/(6 - i)`
​

Answer 1

48/37 + (8/37)i.

Explanation:

8 / (6 - i)

We multiply top and bottom of the fraction by the conjugate of 6 - i , which is 6 + i@

= 8*(6 + i) / (6 - i)(6 + i)

= 48 + 8i / (36 + 6i - 6i - i^2)

= 48 + 8i / (36 - (-1))

= 48 + 8i / 37

= 48/37 + (8/37)i.