Question

How do you simplify `5/(2-i)`?

Answer 1

`2+i`

Explanation:

`5/(2-i)`

Multiply numerator and denominator by the denominator's conjugate:
`=5/(2-i) color(blue)(* (2+i)/(2+i))`

Simplify:
`=(10+5i)/(4-i^2)`

`=(10+5i)/(4+1)`

`=(10+5i)/5`

`=2+i`