Answer
$\dfrac{2+3i}{2+i}=\dfrac{7}{5}+\dfrac{4}{5}i$
Work Step by Step
$\dfrac{2+3i}{2+i}$
Multiply the numerator and the denominator by the complex conjugate of the denominator:
$\dfrac{2+3i}{2+i}=\dfrac{2+3i}{2+i}\cdot\dfrac{2-i}{2-i}=\dfrac{(2+3i)(2-i)}{2^{2}-i^{2}}=...$
$...=\dfrac{4-2i+6i-3i^{2}}{4-i^{2}}=\dfrac{4+4i-3i^{2}}{4-i^{2}}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=\dfrac{4+4i-3(-1)}{4-(-1)}=\dfrac{4+3+4i}{4+1}=\dfrac{7+4i}{5}=\dfrac{7}{5}+\dfrac{4}{5}i$
