Question

Perform the operation and write the result in standard form
3i/3+i+8/3-i

Answer 1

2.7 + 1.7i

We require the fractions to have a common denominator.

multiply the numerator of the first fraction by (3 - i) and the numerator of the second fraction by (3 + 1)

=
`(3i(3-i)+8(3+i))/((3+i)(3-i))`

=
`(9i-3i^2+24+8i)/(9-i^2)`

[ note that i² = (
`√((-1)^2)` = - 1]

=
`(17i+27)/(10)` = 2.7 + 1.7i ← in standard form