Question

Find the quotient. 9-6i/5+3i

Answer 1

see explanation

Explanation:

We require to rationalise the denominator by multiplying the numerator and denominator by the complex conjugate of the denominator.

The conjugate of 5 + 3i is 5 - 3i

noting that i² = - 1, hence

`((9-6i)(5-3i))/((5+3i)(5-3i))` ← expand factors

=
`(45-57i+18i^2)/(25-9i^2)`

=
`(45-57i-18)/(25+9)`

=
`(27-57i)/(34)`

=
`(27)/(34)` -
`(57)/(34)` i ← quotient