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
  i.