let z= (4+3i)/(3-4i) - (2+i)/(1-2i)

First lest us simplify:

==> z= (4+3i)(3+4i)/(3-4i)(3+4i) - (2+i)(1+2i)/(1-2i)(1+2i)

==> z= (12+25i-12)/(3^2 +4^2) - (2+3i -2)/(1^2 + 2^2)

==> z= 25i/25 - 3i/3

==> z= i -i = 0

==> z= 0 + 0i

let z= (4+3i)/(3-4i) - (2+i)/(1-2i)

First lest us simplify:

==> z= (4+3i)(3+4i)/(3-4i)(3+4i) - (2+i)(1+2i)/(1-2i)(1+2i)

==> z= (12+25i-12)/(3^2 +4^2) - (2+3i -2)/(1^2 + 2^2)

==> z= 25i/25 - 3i/3

==> z= i -i = 0

==> z= 0 + 0i