Answer:
[tex]\frac{(5+2i)(6-4i)}{(2+i)}=\frac{68}{5}-\frac{54i}{5}[/tex]
Step-by-step explanation:
We need to find [tex]\frac{(5+2i)(6-4i)}{(2+i)}[/tex]
Solving
[tex]\frac{(5+2i)(6-4i)}{(2+i)}=\frac{(30-20i+12i-8i^2)}{(2+i)}=\frac{(30-8i-8(-1))}{(2+i)}=\frac{(38-8i)}{(2+i)}\\\\\frac{(38-8i)}{(2+i)}=\frac{(38-8i)(2-i)}{(2+i)(2-i)}=\frac{(76-38i-16i+8i^2)}{(4-2i+2i-i^2)}=\frac{(76-54i+8(-1))}{(4-(-1)))}=\frac{(68-54i)}{5}=\frac{68}{5}-\frac{54i}{5}[/tex]
So, [tex]\frac{(5+2i)(6-4i)}{(2+i)}=\frac{68}{5}-\frac{54i}{5}[/tex]
