Question

3+2i/6+5i simplify using i

Answer 1

`(28)/(61)` -
`(3)/(61)` i

Explanation:

Given

`(3+2i)/(6+5i)`

Rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator

The conjugate of 6 + 5i is 6 - 5i, thus

=
`((3+2i)(6-5i))/((6+5i)(6-5i))` ← expand numerator / denominator using FOIL

=
`(18-3i-10i^2)/(36-25i^2)` → simplify using i² = - 1

=
`(18-3i+10)/(36+25)`

=
`(28-3i)/(61)`

=
`(28)/(61)` -
`(3)/(61)` i

Answer 2

28 - 3i / 61

Explanation:

Though the answer above is correct, in order to fit the layout of the question, the fraction has to be condensed. If you insert the answer the way I typed it, it should be correct.

Hope this helps.