Question 915479
Expanding the numerator


{{{z= ((3+4i)(12-5i))/(2+i)=(36-15i+48i-20i^2)/(2+i) }}}


{{{z=(56+33i)/(2+i)=((56+33i)(2-i))/(2^2+1^2)}}}


{{{z=(112-56i+66i-33i^2)/5=(145+10i)/5}}}


{{{z=29+2i}}}


{{{abs(z)=sqrt(29^2+2^2)=13sqrt(5)}}}

{{{Re(z)=29}}}
{{{Im(z)=2}}}