Question

Write the quotient as a +bi 4+6i/ 2-3i​

Answer 1

-
`(10)/(13)` +
`(24)/(13)` i

Explanation:

Given

`(4+6i)/(2-3i)`

To rationalise the denominator, multiply the numerator/ denominator by the complex conjugate of the denominator.

The conjugate of 2 - 3i is 2 + 3i, thus

`((4+6i)(2+3i))/((2-3i)(2+3i))` ← expand factors

=
`(8+24i+18i^2)/(4-9i^2)` → i² = - 1

=
`(8+24i-18)/(4+9)`

=
`(-10+24i)/(13)`

= -
`(10)/(13)` +
`(24)/(13)` i

Answer 2

`(4+6i)/(2-3i)=((4+6i)(2+3i))/((2-3i)(2+3i))`

`(8+12i+12i+18i^2)/(4+6i-6i-9i^2)`

`(-10+24i)/(13)`

`\boxed{(-10)/(13)+(24)/(13)i}`