Find multiplicative inverse of 2+3i / 3-2i

We have to eliminate i from the denominator:

(2 + 3 i) / (3 - 2 i) * (3 + 2 i) / (3 + 2 i) =

= (2 + 3 i) * (3 + 2 i) / (9 - 4 i²) = → we use difference of squares

= (6 + 4 i + 9 i + 6 i²) / (9 + 4) = → because : i² = - 1

= (6 + 13 i - 6) / 13 =

= 13 i / 13 = i

Answer: i.