Question

How do you simplify `(6 + 6i ) / (7 + 6i )`?

Answer 1

To simplify this, multiply by the conjugate of 7+6i, that is 7-6i both in the numerator and denominator. The result would be

`(42+42i -36i +36)/(49+36) =(78 -6i)/85`

`=78/85 - 6/85 i`

This can be put in trignometric form `r(cos theta -isin theta)` if required, by solving `rcos theta =78/85` and `rsin theta=- 6/85`.