#### Answer

$\dfrac{6+2i}{1+2i}=2-2i$

#### Work Step by Step

$\dfrac{6+2i}{1+2i}$
Begin the evaluation of the quotient by multiplying the numerator and the denominator by the complex conjugate of the denominator:
$\dfrac{6+2i}{1+2i}\cdot\dfrac{1-2i}{1-2i}=\dfrac{(6+2i)(1-2i)}{1^{2}-(2i)^{2}}=...$
Evaluate the operations indicated in the numerator and in the denominator:
$...=\dfrac{6-12i+2i-4i^{2}}{1-4i^{2}}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=\dfrac{6-12i+2i-4(-1)}{1-4(-1)}=\dfrac{6-10i+4}{1+4}=\dfrac{10-10i}{5}=...$
$...=\dfrac{10}{5}-\dfrac{10}{5}i=2-2i$