Question

How do you simplify `(5-isqrt3)/(5+isqrt3)`?

Answer 1

The simplification `=11/14-(i5sqrt3)/14`

Explanation:

To simplify a complex numbers, we must multiply by the conjugate of the denominator
if `z=z_1/z_2` then `z=(z_1barz_2)/(z_2barz_2)`

In our case `barz_2=5-isqrt3`
`i^2=-1`

so `((5-isqrt3)(5-isqrt3))/((5+isqrt3)(5-isqrt3))=(25-10isqrt3-3)/(25+3)`

`=(22-10isqrt3)/28=11/14-(i5sqrt3)/14`