What is (4-3i)/(2+i)?

Multiply the numerator and denominator by the conjugate of the denominator, $2-i$. The numerator becomes $(4-3i)(2-i)=8-4i-6i+3i^2=8-10i-3=5-10i$. The denominator becomes $(2+i)(2-i)=4-i^2=5$. So the quotient is $\frac{5-10i}{5}=1-2i$, choice D. Choice B ($1+2i$) loses the negative sign on the imaginary part. Choice A ($3-2i$) and choice C ($2-i$) do not satisfy the check: multiplying $2-i$ by $2+i$ gives $5$, not $4-3i$. Always verify a complex quotient by multiplying it by the divisor to recover the numerator.