Question

Find the quotient of (5+2i)(6-4i)/(2+i) and express it in simplest form.

Answer 1

I believe it's 38-8i/2+1

Answer 2

`((5+2i)(6-4i))/((2+i))=(68)/(5)-(54i)/(5)`

Explanation:

We need to find
`((5+2i)(6-4i))/((2+i))`

Solving

`((5+2i)(6-4i))/((2+i))=((30-20i+12i-8i^2))/((2+i))=((30-8i-8(-1)))/((2+i))=((38-8i))/((2+i))\\\\((38-8i))/((2+i))=((38-8i)(2-i))/((2+i)(2-i))=((76-38i-16i+8i^2))/((4-2i+2i-i^2))=((76-54i+8(-1)))/((4-(-1))))=((68-54i))/(5)=(68)/(5)-(54i)/(5)`

So,
`((5+2i)(6-4i))/((2+i))=(68)/(5)-(54i)/(5)`