Question 173856
Division by complex numbers is really multiplication in disguise.
Multiply by the complex conjugate of the denominator.
{{{(6+2i)/(1+i)=((6+2i)/(1+i))*((1-i)/(1-i))}}}
{{{(6+2i)/(1+i)=((6+2i)*(1-i))/((1+i)*(1-i))}}}
Let's work out the numerator first, similar to the FOIL method,
{{{(6+2i)*(1-i)=6-6i+2i-2i^2}}}
{{{(6+2i)*(1-i)=6-4i+2}}}
{{{(6+2i)*(1-i)=8-4i}}}
Next the denominator,
{{{(1+i)*(1-i)=1-i+i-i^2}}}
{{{(1+i)*(1-i)=1-(-1)}}}
{{{(1+i)*(1-i)=2}}}
Now put it all together,
{{{(6+2i)/(1+i)=((6+2i)*(1-i))/((1+i)*(1-i))}}}
{{{(6+2i)/(1+i)=(8-4i)/2}}}
{{{(6+2i)/(1+i)=4-2i}}}