Question

8-i/6+i =(simplified in form a + bi)

Answer 1

`(47)/(37)` -
`(14)/(37)` i

Explanation:

Given

`(8-i)/(6+i)`

Multiply numerator/ denominator by the conjugate of the denominator.

The conjugate of 6 + i is 6 - i, thus

=
`((8-i)(6-i))/((6+i)(6-i))` ← expand numerator/ denominator using FOIL

=
`(48-14i+i^2)/(36-i^2)` → substitute i² = - 1

=
`(48-14i-1)/(36+1)`

=
`(47-14i)/(37)`

=
`(47)/(37)` -
`(14)/(37)` i