Question

How do you simplify `(6 + i )/(6-i)`?

Answer 1

`(6+i)/(6-i)= (35+12i)/37`
`color(white)("XXXXXXXXXXXX")`(although I'm not sure this is "simpler")

Explanation:

We can clear the complex number from the denominator by multiplying by the complex conjugate.

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

`color(white)("XXX")=(36+12i+i^2)/(36-i^2)`

`color(white)("XXX")=(35+12i)/37`