Let z= (7+2i)/(6-3i)

Let us multiply by 6+3i

=> z= (7+2i)(6+3i)/(6-3i)(6+3i)

= (42 + 21i + 12i - 6)/(6^2 + 3^2)

= (36 + 33i)/(45)

==> z= (36/45) + (33/45)i

= (4/5) + (11/25)i

==> z' = (4/5) - (11/25)i

Let z= (7+2i)/(6-3i)

Let us multiply by 6+3i

=> z= (7+2i)(6+3i)/(6-3i)(6+3i)

= (42 + 21i + 12i - 6)/(6^2 + 3^2)

= (36 + 33i)/(45)

==> z= (36/45) + (33/45)i

= (4/5) + (11/25)i

==> z' = (4/5) - (11/25)i